Question

The polynomials (³ + 3² − 3) and (2³ − 5 + ) when divided by ( − 4) leaves the same remainder. The value of a is​

Answer 1

By Remainder Theorem,

R

1

=a(4)

3

+3(4)

2

−3=64a+45 ...(i)

R

2

=2(4)

3

−5(4)+a=128−20+a=108+a ...(ii)

Given: 2R

1

−R

2

=0

∴2(64a+45)−(108+a)=0 (from (i) and (ii))

⇒128a+90−108−a=0

⇒127a=18

a=

127

18

Option B is correct.