## CBSE PRACTICE PAPER MATHS FOR CLASS 10 POLYNOMIALS CHAPTER 2

**Q 1 – If the roots of the quadratic polynomial are equal, where the discriminant D = b ^{2} – 4ac, then (1 Marks)**

**a) D > 0b) D < 0c) D ≥ 0d) D = 0**

**Q 2 – If the sum of the roots is –p and product of the roots is –1/p, then the quadratic polynomial is (1 Marks)**

**a) k(–px ^{2} + x/p + 1)b) k(px^{2} – x/p – 1)c) k(x^{2} + px – 1/p)d) k(x^{2} – px + 1/p)**

**Q 3 – If the zeroes of the quadratic polynomial x^{2} + (a + 1) x + b are 2 and -3, then (1 Marks) (a) a = -7, b = -1 (b) a = 5, b = -1 (c) a = 2, b = -6 (d) a – 0, b = -6**

**Q 4 – If a and b are the zeroes of the polynomial x ^{2}-11x +30, Find the value of a^{3} + b^{3} (1 Marks)**

a.134

b.412

c.256

d.341

**Q 5 – If the polynomial f(x) = x ^{4} -6x^{3} + 16x^{2} – 25x + 10 is divided by another polynomial x^{2} -2x + k, the remainder comes out to be x + a, find k and a. (1 Marks)**

**Q 6 – Find all the zeroes of the polynomial x ^{4} – 3x^{3} + 6x – 4, if two of its zeroes are √2 and -√2 (1 Marks)**

**Q 7 – If α and β are the zeroes of the polynomial ax ^{2} + bx + c, find the value of α^{2} + β^{2} . (1 Marks)**

**Q 8 – If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5,** **then find the polynomial. (1 Marks)**

**Q 9 – If on division of a polynomial p(x) by a polynomial g(x), the quotient is zero,** **what is the relation between the degrees of p(x) and g(x)? (1 Marks)**

**Q 10 – Find the zeroes of the quadratic polynomial 9t ^{2} – 6t + 1 and verify the relationship**

**between the zeroes and the coefficients. (1 Marks)**

**Q 11 – Form a quadratic polynomial whose zeroes are (1 Marks)**

**Q 12 – If one of the zeros of the quadratic polynomial (k – 1)x ^{2} + kx + 1 is -3,**

**then find the value of k. (1 Marks)**

**Q 13 – Find the zeros of the polynomial p(x) = 4x – 12x + 9. (1 Marks)**

**Q 14 – If the polynomial 6x ^{4} + 8x^{3} + 17x^{2} + 21x + 7 is divided by another polynomial**

**3x**

^{2}+ 4x + 1, the remainder comes out to be (ax + b), find a and b. (2 Marks)**Q 15 – If -1 and 2 are two zeroes of the polynomial 2x ^{3} – x^{2} – 5x – 2, find its third zero. (2 Marks)**

**Q 16 – If 2 and -3 are the zeroes of the quadratic polynomial x ^{2} + (a + 1) x + b; then find the values of a and b. (2 Marks)**

**Q 17 – If one zero of the polynomial 2x ^{2} + 3x + λ is 1/2 find the value of and other zero. (2 Marks)**

**Q 18 – Find the zeros of the polynomial f(x) = x ^{3} – 5x^{2} – 2x + 24, if it is given that the product**

**of its two zeros is 12.(2 marks)**

**Q 19 – If one zero of polynomial (a ^{2} + 9)x^{2} + 13x + 6a is reciprocal of the other,**

**find the value of a. (2 Marks)**

**Q 20 – Divide 2x ^{4} – 9x^{3} + 5x^{2} + 3x – 8 by x^{2} – 4x+ 1 and verify the division algorithm. (2 Marks)**

**Q 21 – On dividing the polynomial 4x ^{4} – 5x^{3} – 39x^{2} – 46x – 2 by the polynomial g(x),**

**the quotient and remainder were x**

^{2}– 3x – 5 and -5x + 8 respectively. Find g(x). (2 Marks)**Q 22 – What must be subtracted or added to p(x) = 8 x ^{4} + 14x^{3} – 2x^{2} + 8x – 12**

**so that 4x**

^{2}+ 3x – 2 is a factor of p(x)? (3 Marks)**Q 23 – On dividing 3x ^{3} + 4x^{2} + 5x – 13 by a polynomial g(x) the quotient and remainder**

**were 3x +10 and 16x – 43 respectively. Find the polynomial g(x). (3 Marks)**

**Q 24 – What must be subtracted from p(x) = 8x ^{4} + 14x^{3} – 2x^{2} + 7x – 8 so that the resulting**

**polynomial is exactly divisible by g(x) = 4x**

^{2}+ 3x – 2? (3 Marks)**Q 25 – If the polynomial f(x) = x ^{4} – 6x^{3} + 16x^{2} – 25x + 10 is divided by another polynomial**

**x**

^{2}– 2x + k, the remainder comes out to be x + a. Find k and a. 3 Marks)**Q 26 – Find the zeros of the polynomial f(x) = – 12x ^{2} + 39x – 28, if it is given**

**that the zeros are in AP. (3 Marks)**

**Q 27 – If ** ** and β are the zeros of the quadratic polynomial f (x) = ax ^{2} + bx + c, then evaluate: (3 Marks)**

**Q 28 – If the zeros of the polynomial f(x) = ax ^{3} + 3bx^{2} + 3cx + d are in A.P.,**

**prove that 2b**

^{3}– 3abc + a^{2}d = 0. (3 Marks)**Q 29 – If two zeros of the polynomial f(x) = x ^{4} – 6x^{3} – 26x^{2} + 138x – 35 are 2 ,find other zeros. (3 Marks)**

**Q 30 – Given that x-** ** is a factor of the cubic polynomial x ^{3} – 3**

**x**

^{2}+ 13x – 3, find all the zeroes of the polynomial. (3 Marks)