Question

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.

Answer 1

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 = \(\frac{-13}{3}\)