- A0
- B1
- C2
- D-1
If the zeros are equal in magnitude but opposite in sign (e.g., alpha and -alpha), their sum is 0. For kx² + 2x - 3k, the sum of zeros is -b/a = -2/k. Setting this to 0, -2/k = 0, which implies that the numerator must be 0, which is impossible. This means 'k' cannot be a non-zero value for the sum to be 0. If k=0, it's not a quadratic polynomial. Let's recheck this. If k is zero, the polynomial is 2x = 0, which has one zero x=0. This satisfies the condition 'equal in magnitude but opposite in sign' (0 and -0). However, the question states it's a quadratic polynomial, implying k cannot be 0. The problem is that if sum of zeros is 0, then -b/a = 0, implying b=0. In this case, 2x is the 'b' term. So for sum of zeros to be zero, 2 must be 0, which is impossible. Let's consider the options. If k=0, it's not a quadratic. Let's reformulate: "If the zeros of the quadratic polynomial P(x) = x² + (k-2)x + (3k-1) are such that one is the negative of the other, what is the value of k?" If one zero is the negative of the other, then their sum is 0. alpha + (-alpha) = 0. From P(x), sum of zeros = -(k-2)/1 = -(k-2). So, -(k-2) = 0, which means k-2 = 0, so k = 2.
More Questions on Polynomials
1**Question 50 (Final Redraft):** If the zeros of the quadratic polynomial P(x) = (k-1)x² - 5x + (2k+1) are reciprocal of each other, then the value of k is:
→ 2**Question (Redrafted and Corrected):** If the zeros of the quadratic polynomial kx² + 2x - 3k are equal in magnitude but opposite in sign, then the value of k is:
→ 3How many real zeros does the polynomial P(x) = (x² - 4)(x + 1)² have?
→ 4For a quadratic polynomial P(x) = ax² + bx + c, the vertex of its parabolic graph is at x =:
→ 5If x = 0 is a zero of the polynomial P(x) = ax² + bx + c, then:
→ 6The constant term of a polynomial P(x) can be found by evaluating:
→ 7If alpha and beta are the zeros of the polynomial P(x) = x² + x - 2, then (1/alpha + 1/beta) is equal to:
→ 8If P(x) is a polynomial such that P(x) = P(-x) for all x, then P(x) is an:
→ 9If a polynomial has real coefficients, its complex non-real zeros always occur in:
→ 10The maximum number of terms in a cubic polynomial is:
→ 11If alpha and beta are the zeros of a polynomial P(x) such that alpha + beta = 5 and alpha * beta = 6, then P(x) is:
→ 12Which of the following statements about polynomial P(x) = x² + 1 is true?
→ 13Let's try: If the product of the zeros of P(x) = kx² + 6x + 8 is 4, then the value of k is:
→ 14If the product of the zeros of P(x) = x² + mx - 16 is 4, then the value of m is:
→ 15If the product of the zeros of P(x) = x² + mx + 16 is 4, then the value of m is:
→ 16The number of real zeros of the polynomial P(x) = (x² + 1)(x - 3) is:
→ 17Which of the following cannot be the graph of a quadratic polynomial?
→ 18If a and b are the zeros of the polynomial x² + px + q, and if a+b = ab, then which of the following is true?
→ 19If one zero of the polynomial P(x) = ax² + bx + c is '0', then:
→ 20The graph of a linear polynomial P(x) = ax + b (where a != 0) is always a:
→ 21For a quadratic polynomial P(x) = ax² + bx + c, if b² - 4ac = 0, then the polynomial has:
→ 22What is the maximum number of terms in a polynomial of degree 'n' if all coefficients are non-zero?
→ 23If one zero of the polynomial P(x) = x³ + 3x² - x - 3 is 1, find the other two zeros.
→ 24If a real number 'a' is a zero of a polynomial P(x), then which of the following is always true?
→ 25If alpha and beta are the zeros of the polynomial P(x) = x² - 8x + 16, what is the value of P(alpha + beta)?
→ 26How many terms are there in the polynomial 5x⁴ - 2x³ + 7x² - x + 10?
→ 27Which of the following is NOT a polynomial in one variable?
→ 28If the sum of the zeros of the polynomial P(x) = x² - 2x + (2k-1) is equal to their product, then the value of k is:
→ 29Which of the following polynomials could have zeros -1/2, 1, and 2?
→ 30If the polynomial P(x) = x³ + 4x² - 3x - 18 is exactly divisible by (x - 2), then which of the following is also a factor?
→ 31If the quadratic polynomial P(x) = kx² + 4x + 1 has equal real zeros, then k must be:
→ 32A quadratic polynomial P(x) has no real zeros. Which of the following is true about its graph?
→ 33If alpha and beta are the zeros of the polynomial 2x² + 5x + k, and alpha² + beta² + alpha*beta = 21/4, what is the value of k?
→ 34The degree of the zero polynomial (P(x) = 0) is:
→ 35If the zeros of a quadratic polynomial are (2+sqrt(3)) and (2-sqrt(3)), then the polynomial is:
→ 36A quadratic polynomial whose zeros are 5 and -2 is:
→ 37When x³ - 2x² + kx + 5 is divided by (x-2), the remainder is 1. Find the value of k.
→ 38If alpha and beta are the zeros of the polynomial P(x) = 2x² + 7x + 3, what is the value of alpha² + beta²?
→ 39If sqrt(5) is a zero of the polynomial f(x) = x² - 5, what is its other zero?
→ 40If the graph of a quadratic polynomial ax² + bx + c opens downwards, which of the following is definitely true?
→ 41A polynomial of degree 4 can have at most how many points of intersection with the x-axis?
→ 42What is the degree of the polynomial P(x) = (x² + 1)(x - 2) - (x³ + 5x)?
→ 43If (x-1) and (x+1) are factors of P(x) = ax³ + bx² + cx + d, then which of the following statements must be true?
→ 44If one zero of the cubic polynomial P(x) = x³ + ax² + bx + c is -1, and the product of the other two zeros is 3, what is the value of 'c'?
→ 45If x = -1 is a zero of the polynomial P(x) = ax³ + bx² + cx + d, then which of the following is true?
→ 46What is the minimum number of real roots a cubic polynomial can have?
→ 47What is the maximum number of real roots a cubic polynomial can have?
→ 48If the sum of two zeros of the polynomial P(x) = x³ - 5x² + kx - 7 is 3, what is the value of k?
→ 49What is the remainder when x³ - ax² + 6x - a is divided by (x - a)?
→ 50For a quadratic polynomial ax² + bx + c whose graph opens upwards and intersects the x-axis at two distinct points, which of the following is true?
→ 51The number of polynomials having zeros -2 and 5 is:
→ 52If alpha and beta are the zeros of the quadratic polynomial P(x) = x² - 6x + 4, find a quadratic polynomial whose zeros are 3alpha and 3beta.
→ 53If (x+a) is a factor of the polynomial 2x² + 2ax + 5x + 10, then the value of a is:
→ 54If a zero of the polynomial f(x) = x² - 5x + 2k is 2, then the value of k is:
→ 55A polynomial of degree 'n' has at most:
→ 56Assertion (A): If P(x) = ax² + bx + c has real zeros, then b² - 4ac >= 0. Reason (R): The discriminant (b² - 4ac) determines the nature of the zeros of a quadratic polynomial.
→ 57If the sum of the zeros of the polynomial f(x) = 2x² - 3kx + 5 is 3, what is the value of k?
→ 58If alpha and beta are the zeros of the polynomial P(x) = x² - x - 4, what is the value of (1/alpha + 1/beta - alpha*beta)?
→ 59If two zeros of the polynomial P(x) = x⁴ - 6x³ - 26x² + 138x - 35 are (2 + sqrt(3)) and (2 - sqrt(3)), find the other two zeros.
→ 60Which of the following expressions is NOT a polynomial?
→ 61If one zero of the quadratic polynomial P(x) = (k²+4)x² + 13x + 4k is the reciprocal of the other, find the positive value of k.
→ 62If alpha, beta, gamma are the zeros of the polynomial P(x) = x³ - 6x² + 11x - 6, then what is the value of (alpha*beta + beta*gamma + gamma*alpha)?
→ 63If alpha and beta are the zeros of the polynomial f(x) = x² - px + q, find a polynomial whose zeros are 1/alpha and 1/beta.
→ 64When a polynomial P(x) = x³ - 3x² + x + 2 is divided by a polynomial G(x), the quotient is x - 2 and the remainder is -2x + 4. What is G(x)?
→ 65If alpha and beta are the zeros of the quadratic polynomial P(x) = x² - 5x + k, and alpha - beta = 1, what is the value of k?
→ 66What is the degree of the polynomial P(x) = (x² + 3x + 1)(2x² - x + 5)?
→ 67If one zero of the polynomial p(x) = x² - (a+1)x + 5 is 5, then the other zero is:
→ 68The number of real zeros of the polynomial f(x) = (x-1)² + 1 is:
→ 69If the zeros of the polynomial x² + px + q are reciprocal of each other, then:
→ 70Which of the following polynomials is a linear polynomial?
→ 71If the product of two zeros of the polynomial x³ - 5x² - 2x + 24 is 12, then the third zero is:
→ 72If two zeros of the polynomial x⁴ - 6x³ - 26x² + 138x - 35 are (2 + sqrt(3)) and (2 - sqrt(3)), then the other two zeros are:
→ 73Assertion (A): If the zeros of the polynomial x² + px + q are twice the zeros of 2x² - 5x - 3, then p = 5 and q = -18. Reason (R): For a quadratic polynomial ax² + bx + c, sum of zeros = -b/a and product of zeros = c/a.
→ 74The sum of the zeros of the polynomial x² + 2x - 8 is:
→ 75If x² - 3 is a factor of x⁴ - 2x³ - 5x² + 6x + 9, then the other factors are:
→ 76The maximum number of times a polynomial of degree n can intersect the x-axis is:
→ 77How many zeros does the polynomial x² + 1 have?
→ 78If alpha and beta are the zeros of the polynomial f(x) = x² - (p+1)x + 5, and alpha + beta = alpha * beta, then the value of p is:
→ 79If alpha and beta are the zeros of the polynomial 2x² - x - 6, then a polynomial whose zeros are 1/alpha and 1/beta is:
→ 80The graph of a linear polynomial ax+b is a straight line which intersects the x-axis at:
→ 81What is the common zero of the polynomials x² - 4 and x² + x - 6?
→ 82The sum of the zeros of the cubic polynomial 2x³ - x² + 5x - 7 is:
→ 83If one zero of the polynomial p(x) = x² + (3k+1)x + k is 2, then the value of k is:
→ 84A polynomial of degree 4, with real coefficients, can have at most how many real roots?
→ 85If alpha and beta are the zeros of the quadratic polynomial x² - 3x + 2, then the value of (alpha + beta)² - 2alpha*beta is:
→ 86If the zeros of the quadratic polynomial x² + (a+1)x + b are 2 and -3, then:
→ 87The number of polynomials whose zeros are 3 and -4 is:
→ 88If alpha, beta, gamma are the zeros of the polynomial 3x³ - 5x² - 11x - 3, then alpha*beta*gamma is:
→ 89If x+1 is a factor of the polynomial x³ + kx² - x + 2, then the value of k is:
→ 90If the polynomial x⁴ + ax³ + 2x² + bx + 1 is divided by x-1 and x+1, the remainders are 5 and 7 respectively. The values of a and b are:
→ 91The number of zeros of the polynomial whose graph is parallel to the x-axis and passes through (0, 3) is:
→ 92If alpha and beta are the zeros of the polynomial P(x) = x² - 4x + 3, then a polynomial whose zeros are 1/alpha and 1/beta is:
→ 93A quadratic polynomial has at most:
→ 94If alpha and beta are the zeros of the polynomial x² + 7x + 10, then the value of 1/alpha + 1/beta is:
→ 95If the zeros of the quadratic polynomial ax² + bx + c are equal, then:
→ 96The value of the polynomial 2x³ - 3x² + 4x - 5 at x = 1 is:
→ 97If the polynomial x³ - x² - ax + b is divisible by (x-1) and (x+1), the values of a and b are:
→ 98If the polynomial x³ + x² - ax + b is divisible by (x-1) and (x+1), the values of a and b are:
→ 99If alpha and beta are zeros of the polynomial f(x) = x² - 8x + k, such that alpha² + beta² = 40, then k = ?
→ 100A quadratic polynomial, one of whose zeros is 2 - sqrt(5) and the sum of its zeros is 4, is:
→ 101If alpha and beta are the zeros of x² - 5x + 6, then the polynomial whose zeros are alpha+1 and beta+1 is:
→ 102For what value of k is -4 a zero of the polynomial x² - x - (2k+2)?
→ 103If alpha and beta are the zeros of the polynomial P(x) = x² - 6x + a, and 3alpha + 2beta = 16, then the value of 'a' is:
→ 104If alpha and beta are the zeros of the polynomial P(x) = x² - 6x + a, and 3alpha + 2beta = 20, then the value of 'a' is:
→ 105If one zero of the polynomial x² - 4x + 1 is (2 + sqrt(3)), then the other zero is:
→ 106What is the degree of the polynomial 7x³ - 3x⁵ + 2x² + 9?
→ 107The product of the zeros of the quadratic polynomial 3x² + 5x - 2 is:
→ 108If the square of the difference of the zeros of the quadratic polynomial x² + px + 45 is 144, then the value of p is:
→ 109Consider the polynomial P(x) = (x-1)(x+2) and Q(x) = (x-2)(x+1). Which of the following statements is true about their zeros?
→ 110If alpha, beta, gamma are the zeros of the cubic polynomial x³ - 3x² + x + 1, then (alpha*beta + beta*gamma + gamma*alpha) is:
→ 111The minimum number of zeros a cubic polynomial can have is:
→ 112If the polynomial x² + x + k has a zero at x=2, then the value of k is:
→ 113If alpha and beta are the zeros of the polynomial 2x² + 7x - 3, then the value of (alpha + beta) / (alpha * beta) is:
→ 114If a and b are the zeros of the polynomial x² - 1, then a polynomial whose zeros are 2a/b and 2b/a is:
→ 115If (x-2) is a factor of the polynomial x² - ax + b, and a+b=11, then the values of a and b are:
→ 116If (x+1) is a factor of x² - ax - 2b, and 2a + 3b = 4, then the values of a and b are:
→ 117The degree of the polynomial 0x⁵ + 2x² + 3x + 1 is:
→ 118If alpha and beta are the zeros of the polynomial f(x) = ax² + bx + c, then (1/alpha + 1/beta)² is equal to:
→ 119If x² + x - p has a zero at x= -2, then the value of p is:
→ 120The number of real zeros for the polynomial x² + 4 is:
→ 121Which of the following is a zero of the polynomial x³ - 3x² + 4x - 12?
→ 122If alpha and beta are the zeros of 2x² + 5x - 9, then the value of alpha² + beta² is:
→ 123The remainder when x³ + 1 is divided by x + 1 is:
→ 124The product of the zeros of the polynomial P(x) = ax³ + bx² + cx + d is:
→ 125If alpha and beta are the zeros of the quadratic polynomial P(x) = x² - (k-6)x + (2k+1), and alpha + beta = alpha * beta, then the value of k is:
→ 126Which of the following polynomials has -3 as a zero?
→ 127If a polynomial P(x) is divided by x - 1, the remainder is 5. If P(x) is divided by x - 2, the remainder is 10. Then the remainder when P(x) is divided by (x - 1)(x - 2) is:
→ 128The degree of the polynomial (x-1)(x-2)(x-3)(x-4) is:
→ 129A quadratic polynomial, whose sum and product of zeros are 3 and -10 respectively, is:
→ 130If alpha and beta are the zeros of the polynomial f(x) = x² - 5x + k, and alpha - beta = 1, then the value of k is:
→ 131The value of 'm' for which the polynomial x² - (m+4)x + 6 has a zero at x=3 is:
→ 132The value of 'm' for which the polynomial x² - (m+2)x + 6 has a zero at x=3 is:
→ 133If one of the zeros of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it:
→ 134If the sum of the zeros of the polynomial 3x² - (k+6)x + 2k - 1 is -1, then the value of k is:
→ 135If the sum of the zeros of the polynomial 3x² - (k+6)x + 2k - 1 is -3, then the value of k is:
→ 136For a quadratic polynomial ax² + bx + c, if a and c have opposite signs, then the zeros of the polynomial are:
→ 137If alpha and beta are the zeros of the quadratic polynomial f(x) = x² - px + q, then a polynomial having 1/alpha and 1/beta as its zeros is:
→ 138If two zeros of the polynomial x³ - 4x² - 3x + 12 are sqrt(3) and -sqrt(3), then its third zero is:
→ 139The value of the polynomial p(x) = 5x - 4x² + 3 when x = -1 is:
→ 140If -1 is a zero of the polynomial p(x) = ax³ - x² + 5x + 1, then the value of a is:
→ 141A polynomial of degree n has:
→ 142If alpha and beta are zeros of x² + x + 1, then the polynomial whose zeros are 1/alpha and 1/beta is:
→ 143What should be added to the polynomial x² - 5x + 4 so that (x - 3) becomes its factor?
→ 144If alpha and beta are the zeros of the quadratic polynomial f(x) = ax² + bx + c, then alpha/beta + beta/alpha is equal to:
→ 145The number of polynomials having zeros as -2 and 5 is:
→ 146If x+a is a factor of 2x² + 2ax + 5x + 10, then the value of a is:
→ 147Assertion (A): The polynomial x⁴ + 4x² + 5 has two real zeros. Reason (R): The degree of a polynomial is the number of its real zeros.
→ 148If alpha, beta, gamma are the zeros of the polynomial 2x³ + x² - 13x + 6, then alpha*beta + beta*gamma + gamma*alpha is equal to:
→ 149If the polynomial x⁴ + 2x³ + 8x² + 12x + 18 is divided by x² + 5, the remainder comes out to be px + q. The values of p and q are:
→ 150If two of the zeros of a cubic polynomial ax³ + bx² + cx + d are 0, then the third zero is:
→ 151If alpha and beta are the zeros of the polynomial f(x) = x² - 8x + k, such that alpha² + beta² = 40, then the value of k is:
→ 152If the sum of the zeros of the quadratic polynomial kx² + 2x + 3k is equal to their product, then k is equal to:
→ 153If x = 2 and x = 3 are zeros of the polynomial 3x² - 2kx + 2m, then the values of k and m are respectively:
→ 154If alpha and beta are the zeros of the polynomial x² + 6x + 2, then the value of (1/alpha + 1/beta) is:
→ 155A quadratic polynomial, whose zeros are -2 and 5, is:
→ 156If one of the zeros of the quadratic polynomial (k-1)x² + kx + 1 is -3, then the value of k is:
→ 157If the product of two zeros of the polynomial p(x) = x³ - 6x² + 11x - 6 is 2, then the third zero is:
→ 158The maximum number of zeros a cubic polynomial can have is:
→ 159If alpha and beta are the zeros of the quadratic polynomial f(x) = x² - p(x+1) - c, then (alpha + 1)(beta + 1) is equal to:
→ 160The graph of y = p(x) is shown below. How many zeros does the polynomial have? (Assume the graph extends infinitely in the shown pattern)
→ 161If one zero of the polynomial p(x) = (k² + 4)x² + 13x + 4k is the reciprocal of the other, then the value of k is:
→ 162Factorize a⁴ - b⁴.
→ 163The expanded form of (2x + 1)³ is:
→ 164If x - k is a factor of x² + 5x - 6, and k is a positive integer, then k is:
→ 165When x⁵ - 4x³ + 2x + 1 is divided by x - 2, the remainder is:
→ 166If (x - 1) is a factor of p(x) = x² + x + k, then the value of k is:
→ 167If p(x) = x³ + 2x² - 5x - 6, find p(-1).
→ 168The degree of the polynomial x⁵ - x⁴ + x³ - x² + x - 1 is:
→ 169Which of the following is a constant polynomial?
→ 170Factorize 3x² - x - 4.
→ 171If a + b = 10 and a² + b² = 58, find ab.
→ 172Which of the following is an identity?
→ 173If x + 2 is a factor of x³ + kx² + 3x + 6, then k is:
→ 174When x³ - 2x² + x + 1 is divided by x + 2, the remainder is:
→ 175How many zeroes does a linear polynomial have?
→ 176If p(x) = ax - 3 and p(1) = 0, then a is:
→ 177The degree of the polynomial 2x² - 3x⁴ + 7 is:
→ 178Which of the following is a monomial with a variable?
→ 179Factorize 12x² - 7x + 1.
→ 180Without actually calculating the cubes, find the value of (-12)³ + (7)³ + (5)³.
→ 181If x + y + z = 0, then x³ + y³ + z³ is equal to:
→ 182If x - 1 is a factor of 2x² + kx, then k is:
→ 183When x³ - ax² + 6x - a is divided by x - a, the remainder is:
→ 184Which of the following is NOT a zero of the polynomial x² - 4?
→ 185The degree of a non-zero constant polynomial is:
→ 186If p(x) = x² - 4, then p(2) is:
→ 187Factorize 8x³ - y³.
→ 188Factorize x³ + 6x² + 12x + 8.
→ 189Factorize y² - 5y + 6.
→ 190Factorize 49a² - 36b².
→ 191The value of 99² is:
→ 192The value of 103 x 107 using an identity is:
→ 193If a - b = 3 and ab = 4, find a² + b².
→ 194If x + y = 5 and xy = 6, find x² + y².
→ 195If x - a is a factor of p(x), then which of the following is true?
→ 196What is the remainder when 4x³ - 3x² + 2x - 1 is divided by x - 1?
→ 197A polynomial can have more than one zero. Is this statement true or false?
→ 198If p(x) = x³ - x² + x - 1, find p(1).
→ 199The coefficient of y³ in the polynomial 2y² - 7y³ + 5 is:
→ 200What is the degree of the polynomial sqrt(3)x⁴ - 5x + 2?
→ 201The term in a polynomial that does not contain any variable is called a:
→ 202Factorize 5x² - 20x.
→ 203Factorize x² - x - 6.
→ 204Factorize 27x³ + y³.
→ 205Factorize a³ - 8.
→ 206Expand (y - 3)³.
→ 207Expand (x + 2)³.
→ 208Expand (x - 2y + 3z)².
→ 209(a + b + c)² is equal to:
→ 210If x + 1 is a factor of ax³ + x² - 2x + 4a - 9, then a is equal to:
→ 211When x¹00 + 1 is divided by x - 1, the remainder is:
→ 212If x = -2 is a zero of the polynomial p(x) = x + a, then a is:
→ 213If p(y) = y³ - 1, find p(-1).
→ 214The degree of the polynomial 0x⁵ + 2x³ - x + 8 is:
→ 215What is the coefficient of x in the polynomial 5x³ + x² - 2x + 7?
→ 216A polynomial p(x) = cx + d, where c is not equal to 0, is a:
→ 217Which of the following is NOT a polynomial?
→ 218How many zeroes can a non-zero constant polynomial have?
→ 219The remainder when x⁴ + x³ - 2x² + x + 1 is divided by x - 1 is:
→ 220Factorize 2x² + 7x + 3.
→ 221Factorize x² + 5x + 6.
→ 222Expand (x + 2)(x + 5).
→ 223Factorize x² - 16.
→ 224Expand (2a - b)².
→ 225Expand (x + 3)².
→ 226For what value of k is x - 1 a factor of 4x³ + 3x² - 4x + k?
→ 227If x - 2 is a factor of x² - kx + 6, then the value of k is:
→ 228The remainder when x² + 2x + 1 is divided by x - 1 is:
→ 229When x³ + 1 is divided by x + 1, the remainder is:
→ 230Find the zero of the polynomial p(x) = 2x + 6.
→ 231What is the zero of the polynomial p(x) = x - 5?
→ 232If p(x) = 3x - 5, find p(2).
→ 233If p(x) = x² - 2x + 1, find p(0).
→ 234What is the degree of the zero polynomial?
→ 235What is the degree of the polynomial 7y⁵ - 3y² + 4?
→ 236What is the coefficient of x² in the polynomial 3x³ - 2x² + 5x - 1?
→ 237A polynomial with three terms is called a:
→ 238A polynomial of degree 1 is called a:
→ 239Which of the following expressions is a polynomial?
→ 240What is the degree of the polynomial 5?
→ 241If (x – 1/x) = 4, then evaluate (x² + 1/x²) and (x⁴ + 1/x⁴).
→ 242Factorise 64m³ – 343n³
→ 243Factorise 8a³ + b³ + 12a²b + 6ab²
→ 244Without actual division, prove that 2x^4 – 5x^3 + 2x^2 – x + 2 is divisible by x^2 – 3x + 2.
→ 245Evaluate (102)^3 using a suitable identity.
→ 246Factorise x^2 – 1 – 2a – a^2.
→ 247Check whether (7 + 3x) is a factor of (3x^3 + 7x).
→ 248Find the values of a and b so that (2x^3 + a x^2 + x + b) has (x + 2) and (2x – 1) as factors.
→ 249Find the value of x^3 + y^3 + z^3 – 3xyz if x + y + z = 15 and x^2 + y^2 + z^2 = 83
→ 250Calculate the perimeter of a rectangle whose area is 25x^2 - 35x + 12
→ 251Give an example of a monomial and a binomial having degrees of 82 and 99, respectively.
→ 252The value of 104 × 96 is
→ 253The value of 5.63 × 5.63 + 11.26 × 2.37 + 2.37 × 2.37 is
→ 254If one of the factor of x² + x – 20 is (x + 5). Find the other
→ 255If x + 2 is a factor of x³ – 2ax² + 16, then value of a is
→ 256Using a suitable identity, determine the value of (17)³ + (-12)³ + (-5)³
→ 257Find the product: (x – 3y) (x + 3y) (x² + 9y²)
→ 258Factorise: (a – b)³ + (b – c)³ + (c – a)³
→ 259If x + y = 12 and xy = 32, Find the value of x² + y²
→ 260Find the value of x³ + y³ + z³ – 3xyz if x² + y² + z² = 83 and x + y + z = 15
→ 261Find the value of 9x² + 4y² if xy = 6 and 3x + 2y = 12.
→ 262Find a quadratic polynomial, the sum and product of whose zeroes are √2 and -3/2, respectively. Also find its zeroes.
→ 263α and β are zeroes of the quadratic polynomial x² – 6x + y. Find the value of ‘y’ if 3α + 2β = 20
→ 264Find the quadratic polynomial if its zeroes are 0 and √5.
→ 265Find the zeroes of the polynomial 4x^2 – 4x – 8. Also, establish a relationship between the zeroes and coefficients.
→ 266Find the value of "p" from the polynomial x² + 3x + p, if one of the zeroes of the polynomial is 2.
→ 267If the product of zeroes of the polynomial p(x)=3x² + kx − 2 is 2/3 , find the value of k.
→ 268If the zeroes of the quadratic polynomial p(x) = ax² + bx + c are reciprocal of each other, prove that c = a.
→ 269Find a quadratic polynomial whose zeroes are 5 and −3.
→ 270Find the zeroes of the polynomial: p(x) = x² − 7x + 10 and verify the relation between zeroes and coefficients.
→ 271If one zero of the polynomial (a² + 9)x² + 13x + 6a is the reciprocal of the other, find the value of a.
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