Question

The root of the equation $\sqrt{2}{x}^2+7x+5\sqrt{2}=0$ are
(a) $\sqrt{2},\frac{5\sqrt{2}}{2}$
(b) $-\sqrt{2},\frac{5\sqrt{2}}{2}$
(c) $\sqrt{2},\frac{-5\sqrt{2}}{2}$
(d) $-\sqrt{2},\frac{-5\sqrt{2}}{2}$

Answer 1

(d) $-\sqrt{2},\frac{-5\sqrt{2}}{2}$

$$\begin{gathered} \text{Given:} \\ \sqrt{2}{x}^2+7x+5\sqrt{2}=0 \\ \Rightarrow \sqrt{2}{x}^2+5x+2x+5\sqrt{2}=0 \\ \text{⇒}x(\sqrt{2}x+5)+\sqrt{2}(\sqrt{2}x+5)=0 \\ \text{⇒}(\sqrt{2}x+5)(x+\sqrt{2})=0 \\ \text{⇒}x=\frac{-5}{\sqrt{2}}\text{=}\frac{-5}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}\text{=}\frac{-5\sqrt{2}}{2}\text{and}x=-\sqrt{2} \end{gathered}$$