Question

Find the roots of the following quadratic equation by using the quadratic formula
$2x^2-2\sqrt{2}x+1=0$

• A. $-\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}$
• B. $\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}$.
• C. $-\frac{1}{2},\frac{1}{2}$
• D. None of these

Answer 1

The correct option is B $\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}$.

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