Polynomials MCQ Test – Class 10th Mathematics Online Quiz with Score

Q1. Assertion (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.

A A is false but R is true.
B Both A and R are true but R is not the correct explanation of A.
C A is true but R is false.
D Both A and R are true and R is the correct explanation of A.

Q2. When x³ - 2x² + kx + 5 is divided by (x-2), the remainder is 1. Find the value of k.

A -2
B -3
C 3
D 2

Q3. If 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?

A 6
B 12
C 4
D 8

Q4. A quadratic polynomial whose zeros are 5 and -2 is:

A x² + 3x - 10
B x² - 3x - 10
C x² - 7x + 10
D x² + 7x - 10

Q5. The graph of a linear polynomial P(x) = ax + b (where a != 0) is always a:

A Circle
B Straight line
C Hyperbola
D Parabola

Q6. If sqrt(5) is a zero of the polynomial f(x) = x² - 5, what is its other zero?

A 0
B -sqrt(5)
C 5
D -5

Q7. If the graph of a quadratic polynomial ax² + bx + c opens downwards, which of the following is definitely true?

A a > 0
B a < 0
C b² - 4ac > 0
D c > 0

Q8. If a and b are the zeros of the polynomial x² + px + q, and if a+b = ab, then which of the following is true?

A q = -p
B p = 1/q
C p = q
D p = -q

Q9. If (x+a) is a factor of the polynomial 2x² + 2ax + 5x + 10, then the value of a is:

A -2
B 2
C -5
D 5

Q10. Which of the following expressions is NOT a polynomial?

A (x² + 1)(x - 5)
B 1/3 x³ + 4x - 7
C 5x⁴ - 2x^(1/2) + 3
D sqrt(3)x² - 2x + 1

Q11. The sum of the zeros of the polynomial x² + 2x - 8 is:

A 2
B -8
C -2
D 8

Q12. If 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.

A x² - 6x + 12
B x² - 18x + 36
C x² - 18x + 12
D x² - 18x + 4

Q13. A quadratic polynomial P(x) has no real zeros. Which of the following is true about its graph?

A It intersects the x-axis at two distinct points.
B It does not intersect the x-axis at all.
C It touches the x-axis at exactly one point.
D It intersects the x-axis at three points.

Q14. If 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)?

A 11
B 6
C -11
D -6

Q15. If the sum of the zeros of the polynomial f(x) = 2x² - 3kx + 5 is 3, what is the value of k?

A 6
B 2
C -2
D -6

Q16. What is the degree of the polynomial P(x) = (x² + 1)(x - 2) - (x³ + 5x)?

A 1
B 0
C 2
D 3

Q17. If a real number 'a' is a zero of a polynomial P(x), then which of the following is always true?

A Both B and C
B x - a is a factor of P(x)
C P(a) = a
D P(a) = 0

Q18. Which of the following is NOT a polynomial in one variable?

A 5x³ - 7x + 1/x
B 10
C (z+1)(z-1)
D y² + sqrt(3)y - 4

Q19. If the sum of two zeros of the polynomial P(x) = x³ - 5x² + kx - 7 is 3, what is the value of k?

A 7
B -19/2
C 19/2
D 5

Q20. If alpha and beta are the zeros of the polynomial 2x² - x - 6, then a polynomial whose zeros are 1/alpha and 1/beta is:

A 2x² - x - 6
B 6x² - x - 2
C 6x² - x + 2
D 6x² + x - 2

Polynomials — MCQ Test

Ready to test yourself?