Question

Le p(x) te a polynomial such that when p(x) is divided by (7-19), the remainder is 99 and
when p(x) is divided by (3-09), the remainder is 19. The remainder when p(x) is divided by
(x-19)(x-99) is
I​

Answer 1

Explanation:

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Answer 2

Answer:-

Let the polynomial be f(x)×(x−19)(x−99)+(ax+b)

Where, ax+b is the remainder.

Now, according to the remainder theorem,

p(19)=99 or

⇒ 19a+b=99 ----- ( 1 )

p(99)=19

⇒ 99a+b=19 ----- ( 2 )

Subtracting ( 2 ) from ( 1 ) we get,

⇒ −80a=80

⇒ a=−1

Substituting value of a in ( 1 ) we get,

⇒ −19+b=99

⇒ b=118

The required remainder =(ax+b)=−x+118.

Explanation:-

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