- A6
- B11
- C-6
- D-11
For a cubic polynomial ax³ + bx² + cx + d, the sum of products of zeros taken two at a time is given by c/a. Here, a=1, c=11, so the value is 11/1 = 11.
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:
→ 3If the zeros of the quadratic polynomial kx² + 2x - 3k are equal in magnitude but opposite in sign, then the value of k is:
→ 4How many real zeros does the polynomial P(x) = (x² - 4)(x + 1)² have?
→ 5For a quadratic polynomial P(x) = ax² + bx + c, the vertex of its parabolic graph is at x =:
→ 6If x = 0 is a zero of the polynomial P(x) = ax² + bx + c, then:
→ 7The constant term of a polynomial P(x) can be found by evaluating:
→ 8If alpha and beta are the zeros of the polynomial P(x) = x² + x - 2, then (1/alpha + 1/beta) is equal to:
→ 9If P(x) is a polynomial such that P(x) = P(-x) for all x, then P(x) is an:
→ 10If a polynomial has real coefficients, its complex non-real zeros always occur in:
→ 11The maximum number of terms in a cubic polynomial is:
→ 12If alpha and beta are the zeros of a polynomial P(x) such that alpha + beta = 5 and alpha * beta = 6, then P(x) is:
→ 13Which of the following statements about polynomial P(x) = x² + 1 is true?
→ 14Let's try: If the product of the zeros of P(x) = kx² + 6x + 8 is 4, then the value of k is:
→ 15If the product of the zeros of P(x) = x² + mx - 16 is 4, then the value of m is:
→ 16If the product of the zeros of P(x) = x² + mx + 16 is 4, then the value of m is:
→ 17The number of real zeros of the polynomial P(x) = (x² + 1)(x - 3) is:
→ 18Which of the following cannot be the graph of a quadratic polynomial?
→ 19If a and b are the zeros of the polynomial x² + px + q, and if a+b = ab, then which of the following is true?
→ 20If one zero of the polynomial P(x) = ax² + bx + c is '0', then:
→ 21The graph of a linear polynomial P(x) = ax + b (where a != 0) is always a:
→ 22For a quadratic polynomial P(x) = ax² + bx + c, if b² - 4ac = 0, then the polynomial has:
→ 23What is the maximum number of terms in a polynomial of degree 'n' if all coefficients are non-zero?
→ 24If one zero of the polynomial P(x) = x³ + 3x² - x - 3 is 1, find the other two zeros.
→ 25If a real number 'a' is a zero of a polynomial P(x), then which of the following is always true?
→ 26If alpha and beta are the zeros of the polynomial P(x) = x² - 8x + 16, what is the value of P(alpha + beta)?
→ 27How many terms are there in the polynomial 5x⁴ - 2x³ + 7x² - x + 10?
→ 28Which of the following is NOT a polynomial in one variable?
→ 29If 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:
→ 30Which of the following polynomials could have zeros -1/2, 1, and 2?
→ 31If the polynomial P(x) = x³ + 4x² - 3x - 18 is exactly divisible by (x - 2), then which of the following is also a factor?
→ 32If the quadratic polynomial P(x) = kx² + 4x + 1 has equal real zeros, then k must be:
→ 33A quadratic polynomial P(x) has no real zeros. Which of the following is true about its graph?
→ 34If 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?
→ 35The degree of the zero polynomial (P(x) = 0) is:
→ 36If the zeros of a quadratic polynomial are (2+sqrt(3)) and (2-sqrt(3)), then the polynomial is:
→ 37A quadratic polynomial whose zeros are 5 and -2 is:
→ 38When x³ - 2x² + kx + 5 is divided by (x-2), the remainder is 1. Find the value of k.
→ 39If alpha and beta are the zeros of the polynomial P(x) = 2x² + 7x + 3, what is the value of alpha² + beta²?
→ 40If sqrt(5) is a zero of the polynomial f(x) = x² - 5, what is its other zero?
→ 41If the graph of a quadratic polynomial ax² + bx + c opens downwards, which of the following is definitely true?
→ 42A polynomial of degree 4 can have at most how many points of intersection with the x-axis?
→ 43What is the degree of the polynomial P(x) = (x² + 1)(x - 2) - (x³ + 5x)?
→ 44If (x-1) and (x+1) are factors of P(x) = ax³ + bx² + cx + d, then which of the following statements must be true?
→ 45If 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'?
→ 46If x = -1 is a zero of the polynomial P(x) = ax³ + bx² + cx + d, then which of the following is true?
→ 47What is the minimum number of real roots a cubic polynomial can have?
→ 48What is the maximum number of real roots a cubic polynomial can have?
→ 49If the sum of two zeros of the polynomial P(x) = x³ - 5x² + kx - 7 is 3, what is the value of k?
→ 50What is the remainder when x³ - ax² + 6x - a is divided by (x - a)?
→ 51For 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?
→ 52The number of polynomials having zeros -2 and 5 is:
→ 53If 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.
→ 54If (x+a) is a factor of the polynomial 2x² + 2ax + 5x + 10, then the value of a is:
→ 55If a zero of the polynomial f(x) = x² - 5x + 2k is 2, then the value of k is:
→ 56A polynomial of degree 'n' has at most:
→ 57Assertion (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.
→ 58If the sum of the zeros of the polynomial f(x) = 2x² - 3kx + 5 is 3, what is the value of k?
→ 59If 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)?
→ 60If 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.
→ 61Which of the following expressions is NOT a polynomial?
→ 62If 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.
→ 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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