Question

If $(x-k)$ is the HCF of $x^2+5x+6$ and $x^2-9$, then find the value of a.

• A. -3
• B. 3
• C. 2
• D. -2

Answer 1

The correct option is A -3

Let $f\left(x\right)=x^2+5x+6andg\left(x\right)=x^2-9$.

If (x-k) is the HCF of f(x) and g(x) , then k is zero of both the polynomials f(x) and g(x).

Hence, f(k) = 0
$\Rightarrow k^2+5k+6=0$
$\Rightarrow (k+3)(k+2)=0$
$\Rightarrow k=-2,-3$.

Also, g(k) = 0
$\Rightarrow k^2-9=0$
$\Rightarrow (k-3)(k+3)=0$
$\Rightarrow a=-3,3$.

Hence, k = -3.