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.

Polynomial MCQ Assignments class 10 Mathematics

X Polynomial MCQ Assignments in Mathematics Class X 

1. If α,β are zeroes of the polynomial f(x) = x2 + px + q, then polynomial having 1/α and 1/β as its zeroes is

(a) x2 + qx + p (b) x2 – px + q (c) qx2 + px + 1 (d) px2 + qx + 1

2. If α and β are zeroes of x2 – 4x + 1, then 1/α + 1/β – αβ is

(a) 3 (b) 5 (c) –5 (d) –3

3. The quadratic polynomial having zeroes as 1 and –2 is :

(a) x2 – x + 2 (b) x2 – x – 2 (c) x2 + x – 2 (d) x2 + x + 2

4. If α, β are zeroes of x2 – 6x + k, what is the value of k if 3α+2β=20 ?

(a)–16 (b) 8 (c) 2 (d) –8

5. If one zero of 2x2 – 3x + k is reciprocal to the other, then the value of k is

(a) 2 (b) −23 (c) −32 (d) –3

6. The quadratic polynomial whose sum of zeroes is 3 and product of zeroes is –2 is

(a) x2 + 3x – 2 (b) x2 – 2x + 3 (c) x2 – 3x + 2 (d) x2 – 3x – 2

7. If (x + 1) is a factor of x2 – 3ax + 3a – 7, then the value of a is :

(a)1 (b) –1 (c) 0 (d) –2

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

(a)1 (b) 2(c)3 (d) more than 3

9. The quadratic polynomial p(y) with –15 and–7 as sum and one of the zeroes respectively is :

(a) y2 – 15y – 56 (b) y2 – 15y + 56 (c) y2+ 15y + 56 (d) y2 + 15y – 56

10.The value of p for which the polynomial x3 + 4x2 – px + 8 is exactly divisible by (x – 2) is :

(a) 0 (b) 3 (c) 5 (d) 16

11. If 1 is a zero of the polynomial p(x) = ax2– 3(a – 1)x – 1, then the value of a is :

(a) 1 (b) –1 (c) 2 (d) –2

12. If –4 is a zero of the polynomial x2 – x – (2 + 2k), then the value of k is :

(a) 3 (b) 9 (c) 6 (d) –9

13.The degree of the polynomial (x + 1)(x2 – x – x4 + 1) is : 

 (a) 2 (b) 3 (c) 4 (d) 5

14. If (x + 1) is a factor of x2– 3ax + 3a – 7, then the value of a is :

(a) 1 (b) –1 (c) 0 (d) –2

15. If sum of the squares of zeroes of the quadratic polynomial f(x) = x2 – 8x + k is 40, the value of k is :
(a) 10 (b) 12 (c) 14 (d) 16

X math's Chapter: 02 Polynomials CBSE Test paper New
Class X Polynomial Test Paper-1    Download File

Class X Polynomial Test Paper-2        Download File

Class X Polynomial Test Paper-3         Download File

Class X Polynomial Test Paper-4          Download File

CBSE sample paper 10th Polynomials

1. Find a quadratic polynomial, the sum and product of whose zeroes are 0 and √5 respectively.

2. Find the quadratic polynomial, the sum and product of whose zeroes are 4 and 1, respectively

3. If a andb are the zeros of the quadratic polynomial f(x)= x2-5x+4, find the value of 1/a + 1/b-2a b

4. Find the zeroes of the quadratic polynomial 4 √3 x2 + 5 x - 2 √3 and verify the relationship between the zeroes and the coefficients.

5. Find the zeroes of the quadratic polynomial 4u2 + 8u and verify the relationship between the zeroes and the coefficients

6. Find the quadratic polynomial, the sum and product of whose zeroes are √2 and √3 respectively.

7. If a and b are the zeros of the given quadratic polynomial f(x)= 5x2 - 7x + 1, find the value 1/a + 1/b

8. Find the zeroes of the polynomial x2 – 3 and verify the relationship between the zeroes and the
Coefficients

9. Find the remainder when p(x)= x3-6x2+2x-4 when divided by 1 - 2x.

10. Find the remainder when x51+51 is divided by (x+1).

11. Find all the integral zeros of x3 -3x2 - 2x + 6

12. Obtain all zeros of 3x4 + 6x3 - 2x2 - 10x - 5, if two of its zeros are √5/√3 and - √5/√3

13. If (x - 2) and [x – ½ ] are the factors of the polynomials qx2 + 5x + r prove that q = r

14. If the zeroes of the polynomial are 3x2 − 5x + 2 are a+ b and a- b, find a and b.

15. On dividing 2x2 + 3x + 1 by a polynomial g(x), the quotient and the remainder were 2x-1 and 3 respectively. Find g (x). 

Polynomial test paper for class 10

CBSE TEST PAPER O1 

   10th Polynomial         

1. Write the zeroes of the polynomial x² -2x + 4.

2. Find a quadratic polynomial, the sum and product of whose zeroes are 0 and √5  respectively.

3. Find the quadratic polynomial, the sum and product of whose zeroes are 4 and 1, respectively

4. If a andb are the zeros of the quadratic polynomial f(x)= x²-5x+4, find the value of 1/a  + 1/b-2a b

5. Find the zeroes of the quadratic polynomial 4 √3 x² + 5 x - 2 √3 and verify the relationship between the zeroes and the coefficients.

6. Find the zeroes of the quadratic polynomial 4u² + 8u and verify the relationship between the zeroes and the coefficients

7. Find the quadratic polynomial, the sum and product of whose zeroes are √2 and √3 respectively.

8. If a and b are the zeros of the given quadratic polynomial f(x)= 5x² - 7x + 1, find the value  1/a  + 1/b

9. Find the zeroes of the polynomial x² – 3 and verify the relationship between the zeroes and theCoefficients

10. Find the remainder when p(x)= x³-6x²+2x-4 when divided by  1 - 2x.

11. Find the remainder when x⁵¹+51 is divided by (x+1).

12. Find all the integral zeros of x³ -3x² - 2x + 6

13. Obtain all zeros of 3x⁴ + 6x³ - 2x² - 10x - 5, if two of its zeros are √5/√3 and - √5/√3

14. If (x - 2) and [x – ½ ] are the factors of the polynomials qx² + 5x + r prove that q = r

15. If the zeroes of the polynomial are 3x² − 5x + 2 are a+ b and a- b, find a and  b.

16. On dividing 2x2 + 3x + 1 by a polynomial g(x), the quotient and the remainder were 2x-1 and 3 respectively. Find g (x).