Question

(ii) The polynomials (ax3 + 4x2 + 3x - 4) and
(x2 - 4x + a) when divided by (x - 3) leave the
same remainder. Find the value of a.​

Answer 1

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Let p(x) = ax3 + 4x2 + 3x – 4 and q(x) = x3 – 4x + a be the given  polynomials.

When p(x) and q(x) are divided by (x – 3) the remainder are p(3)  and q(3)  respectively.

p(3) = q(3)  given

a(3)3 + 4(3)2 + 3 × 3 – 4 = 33 – 4 × 3 + a

⇒  27a + 36 + 9 – 4 = 27 – 12 + a

⇒ 26a = 15 – 41

⇒ 26a = - 26

∴    a = - 26/26 = - 1

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