Polynomial class 10 test yourself

 Section-A

1. The zeroes of the quadratic polynomial x² + 99x + 127 are

(A) both positive 

(B) both negative 

(C) one positive and one negative 

(D) both equal

2. The zeroes of the quadratic polynomial x² + k x + k, k ≠ 0,

(A) cannot both be positive 

(B) cannot both be negative 

(C) are always unequal 

(D) are always equal

3. If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then

(A) c and a have opposite signs 

(B) c and b have opposite signs 

(C) c and a have the same sign 

(D) c and b have  the same sign

4. If one of the zeroes of a quadratic polynomial of the form x²+ax + b is the negative of the other, then it

(A) has no linear term and the constant term is negative.
(B) has no linear term and the constant term is positive.
(C) can have a linear term but the constant term is negative.
(D) can have a linear term but the constant term is positive.

5. The number of polynomials having zeroes as –2 and 5 is

(A) 1            (B) 2 

(C) 3            (D) more than 3

Section-B

1. Find the zeroes of 2x³ – 11x² + 17x – 6.

2. Find the quadratic polynomial, the sum and the product of whose zeroes are ¹/₂, and –2 .3. Find the values of m and n for which x = 2 and –3 are zeroes of the polynomial: 3x² – 2mx + 2n.4. Check whether x² + 4 is factor of x⁴ + 9x² + 20

Section-C

5. Divide the polynomial (x⁴ + 1) by (x – 1) and verify the division algorithm.

6. Find all zeroes of x⁴ – 3x³ – 5x² + 21x – 14, if two of its zeroes are √7 and – √7 7. On dividing x³ – 3x² + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4 respectively, find g(x).

Section-D

8. Given that √2 is a zero of the cubic polynomial 6x³ + √2 x² – 10x – 4 √2 , find  its other two zeroes.

9. Find k so that x² + 2x + k is a factor of 2x⁴ + x³ – 14 x² + 5x + 6. Also find all the zeroes of the two polynomials.

10. Given that x – √5 is a factor of the cubic polynomial x³ – 3√ 5x² + 13x – 3 √5 , find all the zeroes of the polynomial.