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If f(x)=(x^(2)+3x+2)(x^(2)-7x+a) and g(x...

If `f(x)=(x^(2)+3x+2)(x^(2)-7x+a)` and `g(x)=(x^(2)-x-12)(x^(2)+5x+b)`, then the value of `a` and `b`, if `(x+1)(x-4)` is H.C.F. of `f(x)` and `g(x)` is

A

`a=10 : b=6`

B

`a=4 : b=12`

C

`a=12 : b=4`

D

`a=6 : b=10`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` According to the equation `x^(2)-7x+a` is divisible by `x-4` and `x^(2)+5x+b` is divisible by `x+1`.
`:.a=12` , `b=4`
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