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Question

If (x - 6) is the HCF of x2 - 2x - 24 and x2- kx - 6, then what is the value of k?

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Solution

Given that (x6) is the HCF of
x22x2y and x24x6(x6) is factor of both expression
Let f(x1)=x212x124
and f(x2)=x224x26
Now f(x1)=f(x2) at (x1=x2=6)
(6)22(6)24=(6)24(6)60=306k6k=30k=5

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