Question

If $(x-\sqrt{2})$ is a factor of $(7x^2-4\sqrt{2}x-a)$, then find $a$.

Answer 1

$g\left(x\right)=7x^2-4\sqrt{2}x-a$

as $(x-\sqrt{2})$ is a factor

$g\left(\sqrt{2}\right)=0=7.2-4.2-a=6-a$

$\Rightarrow a=6$