Question

Find the roots of quadratic equation $\sqrt{2}{x}^2+7x+5\sqrt{2}=0$

Answer 1

Given,

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

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

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

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

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

These are the required roots.