A polynomial leaves a remainder when divided by and a remainder when divided by

MATHEMATICS · Single correct · CBSE · Mathematics · Polynomials · Polynomials

Problem

A polynomial p(x)=ax2+bx+6p(x)=ax^{2}+bx+6 leaves a remainder 44 when divided by (x−1)(x-1) and a remainder −6-6 when divided by (x+2)(x+2). Which ordered pair (a,b)(a,b) satisfies these conditions? (a) (−53,−13)\left(-\dfrac{5}{3},-\dfrac{1}{3}\right) (b) (−4,2)(-4,2) (c) (−83,23)\left(-\dfrac{8}{3},\dfrac{2}{3}\right) (d) (−4,−2)(-4,-2)

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