## Important Questions for Class 10 Maths Chapter 2 Polynomials

Q: If the sum of zeroes of the quadratic polynomial 3x^{2} – kx + 6 is 3, then find the value of k. (2012)

Ans: 9

Q. If α and β are the zeroes of the polynomial ax^{2} + bx + c, find the value of α^{2} + β^{2}. (2013)

Ans:

Q. If the sum of the zeroes of the polynomial p(x) = (k^{2} – 14) x^{2} – 2x – 12 is 1, then find the value of k. (2017 D)

Ans: k = ±4

Q. If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then find the polynomial. (2016 D)

Ans: x^{2} + 6x + 5 = 0

Q. A quadratic polynomial, whose zeroes are -4 and -5, is …. (2016 D)

Ans: x^{2} + 9x + 20

Q. Find the condition that zeroes of polynomial p(x) = ax^{2} + bx + c are reciprocal of each other. (2017 OD)

Ans: Coefficient of x^{2} = Constant term

Q. Form a quadratic polynomial whose zeroes are 3 + √2 and 3 – √2. (2012)

Ans: x^{2} – 6x + 7

Q. Find a quadratic polynomial, the sum and product of whose zeroes are 0 and -√2 respectively. (2015)

Ans: x^{2} – √2

Q. If the zeroes of the polynomial x^{2} + px + q are double in value to the zeroes of 2x^{2} – 5x – 3, find the value of p and q. (2012)

Ans: p = -5, q = -6

Q. What must be subtracted from the polynomial f(x) = x^{4} + 2x^{3} – 13x^{2} – 12x + 21 so that the resulting polynomial is exactly divisible by x^{2} – 4x + 3? (2012, 2017 D)

Ans: (2x – 3) should be subtracted from x^{4} + 2x^{3} – 13x^{2} – 12x + 21.

Q. If a polynomial x^{4} + 5x^{3} + 4x^{2} – 10x – 12 has two zeroes as -2 and -3, then find the other zeroes. (2014)

Ans: x = √2 or x = -√2