If the polynomials 2 x 3 + ax 2 +3 x -5 and x 3 + x 2 -4 x + a leave the same remainder when divided by x -2, find the value of a .

Question

Philoid · Accepted Answer

Let, p (x) = 2x³+ax²+3x-5 and q (x) = x³+x²-4x+a be the given polynomials.

The remainders when p (x) and q (x) are divided by (x – 2) and p (2) and q (2) respectively.

By the given condition, we have:

p (2) = q (2)

2 (2)³ + a (2)² + 3 (2) – 5 = (2)³ + (2)² – 4 (2) + a

16 + 4a + 6 – 5 = 8 + 4 – 8 + a

3a + 13 = 0

3a = - 13

a =

If the polynomials 2x3+ax2+3x-5 and x3+x2-4x+a leave the same remainder when divided by x-2, find the value of a.