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).