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Given f(x) is a cubic polynomial in x . ...

Given f(x) is a cubic polynomial in x . If f(x) is divided by `(x+3),(x+4),(x+5)and (x+6)`, then it leaves the remainders 0, 0 , 4 and 6 respectively . Find the remainder when f(x) is divided by `x+7`.

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

From the given data x +3 and x+4 are two factors of (x).
Let other factor br ax + p
`:.f(x)=(x+4)(ax+p)`
And also given,
`f(-5)=4andf(-6)=6`
`rArr(-2)(-1)(-5a+p)=4`
`rArr-5a+p=2` (1)
and `(-3)(-2)(-6a+p)=6`
`rArr-6a+p=1` (2)
On solving Eqs . (1) and (2) , we get
a=1 and p = 7 .
`:.f(x)=(x+3)(x+4)(x+7)`
`:.f(-7)=0`.
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