If p (x) = 2x 3 + ax 2 + 3x – 5 and q (x) = x 3 + x 2 – 4x + a leave the same remainder when divided by (x – 2), show that

Question

Philoid · Accepted Answer

We have,

p (x) = 2x³ + ax² + 3x – 5

q (x) = x³ + x² – 4x + a

It is given in the question that, when p (x) and q (x) is divided by (x – 2) it leaves same remainder

∴ p (2) = q (2)

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

2 × 8 + a × 4 + 3 × 2 – 5 = 8 + 4 – 4 × 2 + a

16 + 4a + 6 – 5 = 12 – 8 + a

16 + 4a + 1 = 4 + a

4a – a = 4 – 17

3a = - 13

a =

Hence proved

If p (x) = 2x3 + ax2 + 3x – 5 and q (x) = x3 + x2 – 4x + a leave the same remainder when divided by (x – 2), show that