Question

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

Answer 1

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 $f\left(x_1\right)=x_1^2-2x_1-24$

and $f\left(x_2\right)=x_2^2-4x_2-6$

Now $f\left(x_1\right)=f\left(x_2\right)$ at $(x_1=x_2=6)$

$\Rightarrow (6{)}^2-2(6)-24=(6{)}^2-4\left(6\right)-6\Rightarrow 0=30-6k\Rightarrow 6k=30\therefore k=5$