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Class 10 Maths Important questions for Polynomial



1) If the polynomial f(x) = x4 -6x3 + 16x2 – 25x + 10 is divided by another polynomial x2 -2x + k, the remainder comes out to be x + a, find k and a. 2) Find all the zeroes of the polynomial x4 – 3x3 + 6x – 4, if two of its zeroes are √2  and -√2 3) If p and q are he zeroes of the quadratic polynomial f(x) = x2 – 2x + 3, find a polynomial whose roots are:
  1. p + 2, q + 2
  2. (p-1)/(p+1) , (q-1)/(q+1)
4) For what value of k, -7 is the zero of the polynomial 2x2 + 11x + (6k – 3)? Also find the other zero of the polynomial 5) What must be added to f(x) = 4x4 + 2x3 – 2x2 + x – 1 so that the resulting polynomial is divisible by g(x) = x2 + 2x -3? 6) 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. 7) 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
8) Find the zeroes of 2x3 – 11x2 + 17x – 6. 9) If (x - 2) and [x – ½ ] are the factors of the polynomials qx2 + 5x + r prove that q = r 10) Find k so that the polynomial x2 + 2x + k is a factor of polynomial 2x4 + x3 – 14x2 + 5x + 6. Also, find all the zeroes of the two polynomials. 11) On dividing p(x) = x3 – 3x2 + x + 2 by a polynomial q(x), the quotient and remainder were x – 2 and -2x + 4, respectively. Find g(x). 12) a, b, c are zeroes of cubic polynomial x3 – 2x2 + qx – r. If a + b = 0 then show that 2q = r. 13) Find the remainder when x51 +51 is divided by (x+1). 14) a,b and c are zeroes of polynomial x3 + px2 + qx + 2 such that a b + 1 = 0. Find the value of 2p + q + 5. 15) Find the quadratic polynomial, the sum and product of whose zeroes are 4 and 1, respectively Answer 1) k = 5, a = -5 2) √2  , -√2, 2,1 4) -3, 3/2, -7 5) 61x – 65 10) -3, -1/2, 1, 2 11) x2 – x +1 14) 0
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