Question

If $(x-1)$ is a factor of $m{x}^2-\sqrt{2}x+1=0$, then the value of 'm' is:

• A. $\sqrt{2}$
• B. $1$
• C. $\sqrt{2}-1$
• D. $\sqrt{2}+1$

Answer 1

The correct option is C $\sqrt{2}-1$

$(x-1)$ is a factor of $p\left(x\right)=m{x}^2-\sqrt{2}x+1=0$.
Using Factor Theorem,
$p\left(1\right)=0$
$m\times 1^2-\sqrt{2}\times 1+1=0$
$m-\sqrt{2}+1=0$
$m=\sqrt{2}-1$