Question

10. If (x-6) is the HCF of x^2-2x-24 and x^2-kx-6 then the value of 'k' is (a) 3 (b) 5 (c) 6 (d) 8​

Answer 1

Step-by-step explanation:

Given that (x−6) is the HCF of

x

2

−2x−2y and x

2

−4x−6(x−6) is factor of both expression

Let f(x

1

)=x

1

2

−2x

1

−24

and f(x

2

)=x

2

2

−4x

2

−6

Now f(x

1

)=f(x

2

) at (x

1

=x

2

=6)

⇒(6)

2

−2(6)−24=(6)

2

−4(6)−6

⇒0=30−6k⇒6k=30∴k=5