Question

If $x^2-11x+a$ and $x^2-14x+2a$ have a common factor, then what are the values of $a$?

• A. $0,7$
• B. $5,20$
• C. $0,24$
• D. $1,3$

Answer 1

The correct option is C $0,24$

Let $(x-\alpha )$ be the common factor then

${\alpha }^2-11\alpha +a=0\&{\alpha }^2-14\alpha +2a=0$

Subtract 2 eq${}^n$ we get $a=3\alpha$

$\Rightarrow {\alpha }^2-11\alpha +3\alpha =0\Rightarrow \alpha (\alpha -8)=0$

$\Rightarrow \alpha =0,8\Rightarrow a=0,24$