Question

If the polynomial 6
4 − 9
3 − 2
2 + − is exactly divisible by the
polynomial 3
2 − 4 , then find the values of a and b.

Answer 1

Answer:

Given polynomial

p(x)=6x4+8x3−5x2+ax+b

And g(x)=2x2−5

So,

On divide p(x) to g(x) and we get,

Quotient =3x2+4x+5

Reminder=(20+a)x+(25+b)

Given that,

The polynomial 6x4+8x3−5x2+ax+b is exactly divisible by the polynomial 2x2−5.

Hence,

(20+a)x+(25+b)=0

⇒20+a=0

⇒a=−20

And 25+b=0

b=−25