    Question

# Let p(x) be a polynomial such that when p(x) is divided by (x−19), the remainder is 99 and when p(x) is divided by (x−99), the remainder is 19. The remainder when p(x) is divided by (x−19)(x−99) is?

A
(x+80)
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B
(x+80)
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C
(x+118)
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D
(x+118)
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Solution

## The correct option is B (−x+118)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=−1Substituting value of a in ( 1 ) we get,⇒ −19+b=99⇒ b=118The required remainder =(ax+b)=−x+118  Suggest Corrections  0      Similar questions  Related Videos   MATHEMATICS
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