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If x^2-11x+k and x^2-14x+2k have a comm...

If `x^2-11x+k` and `x^2-14x+2k` have a common factor then the non zero value of `k` is: (A) 8 (B) 16 (C) 24 (D) -9

Text Solution

Verified by Experts

Let `x-a` is the common factor of given two polynomials.
then, for `x = a`,
`a^2-11a+k = 0->(1)`
`a^2-14a+2k = 0->(2)`
Subtracting (1) from (2),
`a^2-14a+2k -a^2+11a-k = 0`
`=>-3a = -k`
`=>a = k/3`
...
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