Class X Math
Test For Polynomials
Max Marks : 50
Max Time : 1 hour 10 Mins
1. What is the value of p(x) = x2 – 3x – 4 at x = –1? (3 marks)
2. What is the zero of 2x + 3? (2 marks)
3. The Coefficient of x and the constant term in a linear polynomial are 5 and –3 respectively. Find its zero. (2 marks)
4. Find the product of zeroes of the quadratic polynomial 3x2 + 5x – 2. (2 marks)
5. If a fifth degree polynomial is divided by a quadratic polynomial, write the possible degree of the quotient. (3 marks)
6. For what value of k, (–4) is a zero of the polynomial x2 – x – (2k + 2)? (3 marks)
7. The sum and product of the zeroes of a quadratic polynomial are
and –3 respectively. What is the quadratic polynomial?
(2 marks)
8. If 1 is a zero of the polynomial p(x) = ax2 – 3 (a – 1) x – 1, then find the value of a. (3 marks)
9. Write a quadratic polynomial, the sum and product of whose zeroes are 3 and –2 respectively. (2 marks)
10. If α and β are the zeroes of a quadratic polynomial x
2 + x – 2 then find the value of
(3 marks)
11. If α and β are the zeroes of x
2 + px + q then find the value of
(3 marks)
12. Find the zeroes of 2x2 – 8x + 6. (3 marks)
13. Find the value of ‘k’ such that the quadratic polynomial 3x2 + 2kx + x – k – 5 has the sum of zeroes as half of their product. (3 marks)
14. Find the cubic polynomial whose zeroes are 5, 3 and –2. (3 marks)
15. If 1 is a zero of x3 – 3x2 – x + 3 then find all other zeroes. (2marks)
16. Find all the zeroes of 2x
4 – 3x
3 – 3x
2 + 6x – 2, if two of its zeroes are 1 and
(2 marks)
17. Find the zeroes of the quadratic polynomial 4x2 – 6 – 8x and verify the relationship between the zeroes and the coefficients of the polynomial. (2 marks)
18. Find the zeroes of the quadratic polynomial 4x2 – 6 – 8x and verify the relationship between the zeroes and the coefficients of the polynomial. (2 marks)
19. Find a quadratic polynomial whose zeroes are –12 and 4 and verify the relationship between the zeroes and the coefficients. (3 marks)
20. If the polynomial 4x4 + 6x3 + 13x2 + 20x + 7 is divided by another polynomial 3x2 + 4x + 1 then the remainder comes out to be ax + b, find ‘a’ and ‘b’. (3 marks)