Question

The polynomials ax^3-7x^2+7x-2 and x^3-2ax^2+8x-8 when divided by x-2 leave the same remainder. Find the value of k.

sum no 12 .... please help​

Answer 1

Answer:

$p(x) = a {x}^{3} - 7 {x}^{2} + 7x - 2 \\ p(2) = a {(2)}^{3} - 7( {2)}^{2} + 7(2) - 2 \\ = 8a - 28 + 14 - 2 \\ = 8a - 16$

$q(x) = {x}^{3} - 2a {x}^{2} + 8x - 8 \\ q(2) = 8 - 8a + 16 - 8 \\ = - 8a + 16$

As p(x) and q(x) leaves sames remainder

So p(x) = q(x)

$8a - 16 = - 8a + 16 \\ 8a + 8a = 16 + 16 \\ 16a = 32 \\ a = 16$