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If x^(2) + ax+ b and x^(2) + bx + c have...

If `x^(2) + ax+ b` and `x^(2) + bx + c` have a common factor `(x-k)`, then `k ="_____"`.

A

`(a-b)/(b-c)`

B

`(b-c)/(c-a)`

C

`(c-b)/(b-a)`

D

`(c-b)/(a-b)`

Text Solution

Verified by Experts

The correct Answer is:
D
`x^(2) + ax + b` and `x^(2) + bx + c` have a common factor `(x-k)`.
`rArr k^(2) + ak + b = 0` and `k^(2) + bk + c= 0`
`rArr k^(2) + akl + b = k^(2) + bk + c`
`ak + b = bk + c`
`k = (c-b)/(a-b)`.
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