Question

The given quadratic equations have real roots and the roots are equal and that is $\frac{1}{\sqrt{2}}$ :
$2x^2-2\sqrt{2}x+1=0$

• A. True
• B. False

Answer 1

The correct option is A True

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

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

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

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

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

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

$\Rightarrow$ Hence, we can see roots iven in question is correct.