Question

The polynomial p(x) = 2x^3 + kx^2 - 3x + 5 and q(x) = x^3 + 2x^2 - x + k , when divided by (x-2) leave the same remainder r ¹ and r ² respectively . Find the value of k , if r¹ - r² = 0

Answer 1

put x =2
r1=
$= 2(8) + k(4) - 6 + 5 \\ = 21 - 6 + 4k \\ r1 = 15 + 4k \\ r2 = (8) + 2(4) - 2 + k \\ r2 = 14 + k \\ r1 - r2 = 15 + 4k - 14 - k \\ = 1 + 3k \\ 1 + 3k = 0 \\ 3k = - 1 \\ k = \frac{ - 1}{3}$