Question

If $(x-a)$ is the HCF of
$x^2-x-6and{x}^2+3x-18$ ,
then find the value of a.

• A. -2
• B. -6
• C. -3
• D. 3

Answer 1

The correct option is D 3

Let $f\left(x\right)=x^2-x-6andg\left(x\right)=x^2+3x-18$.

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

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

Also, g(a) = 0
$\Rightarrow a^2+3a-18=0$
$\Rightarrow (a-3)(a+6)=0$
$\Rightarrow a=-6,3$.

Hence, a = 3.