Question

The given quadratic equations have real roots and the roots are $-\sqrt{2},\frac{-5}{\sqrt{2}}$ :
$\sqrt{2}{x}^2+7x+5\sqrt{2}=0$

• A. True
• B. False

Answer 1

The correct option is A True

$\sqrt{2}{x}^2+7x+5\sqrt{2}=0$

$\Rightarrow$ $\sqrt{2}{x}^2+5x+2x+5\sqrt{2}=0$

$\Rightarrow$ $x(\sqrt{2}x+5)+\sqrt{2}(\sqrt{2}x+5)=0$

$\Rightarrow$ $(x+\sqrt{2})(\sqrt{2}x+5)=0$

$\Rightarrow$ $x+\sqrt{2}=0$ and $\sqrt{2}x+5=0$

$\Rightarrow$ $x=-\sqrt{2}$ and $x=\frac{-5}{\sqrt{2}}$

$\therefore$ Here, we can see roots are real and roots are $-\sqrt{2},\frac{-5}{\sqrt{2}}$.