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.also find the remainder in each case

Answer 1

Zero of polynomial x-2= 2

Then,

6+2a+3x-5

= 6+2a+3×2-5

= 6+2a+6-5

=7+2a= Remainder

Again,

3x+2x-4x+a

=3×2+2×2-4×2+a

= 6+4-8+a

=2+a = Remainder

A/Q,

7+2a = 2+a

= 2a-a= 2-7

= a= -5

So, a= -5

Then,

Remainder= 7+ 2×(-5)

= 7-10= -3

Again,

Remainder= 2+(-5)= -3

Thus, the remainders are same.