If (x-k) is a common factor of x^(2)+3x+...

If `(x-k)` is a common factor of `x^(2)+3x+aandx^(2)+4x+b`, then find the value of k in terms of a and b .

A

a + b

B

a - b

C

2a + 3b

D

2 a - 3 b

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The correct Answer is:

B

Given x - k is a common factor of `x^(2)+3x+a and x^(2)+4x+b`.
`:.(k)^(2)+3k+a=0 and (k)^(2)+4k+b=0`
`rArrk^(2)+4k+b=k^(2)+3k+a`
`rArrk=a-b`.

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