Question

On solving the following quadratic equation by factorization, the roots are $\sqrt{2}$, $1$:
$x^2-(\sqrt{2}+1)x+\sqrt{2}=0$

• A. True
• B. False

Answer 1

The correct option is A True

$x^2-(\sqrt{2}+1)x+\sqrt{2}=0$

$\Rightarrow$ $x^2-\sqrt{2}x-x+\sqrt{2}=0$

$\Rightarrow$ $x(x-\sqrt{2})-1(x-\sqrt{2})=0$

$\Rightarrow$ $(x-\sqrt{2})(x-1)=0$

$\Rightarrow$ $x-\sqrt{2}=0$ and $x-1=0$

$\Rightarrow$ $x=\sqrt{2}$ and $x=1$

$\therefore$ The given roots in question are correct.