root 2 X square + 7 x + 5 root 2 is equal to zero solve the following

1.	root 2 X square + 7 x + 5 root 2 is equal to zero solve the following quadratic equation and find the root by factorization
Answer» $\textbf{Given:}$ $\sqrt{2}x^2+7x+5\sqrt{2}=0$ $\textbf{To find:}$ $\text{Roots of the given quadratic equation}$ $\textbf{Solution:}$ $\text{Consider,}$ $\sqrt{2}x^2+7x+5\sqrt{2}=0$ $\sqrt{2}x^2+2x+5x+5\sqrt{2}=0$ $\sqrt{2}x(x+\sqrt{2})+5(x+\sqrt{2})=0$ $(\sqrt{2}x+5)(x+\sqrt{2})=0$ $\sqrt{2}x+5=0\;\text{(or)}\;x+\sqrt{2}=0$ $\implies\,x=\dfrac{-5}{\sqrt{2}}\;\text{(or)}\;x=-\sqrt{2}$ $\therefore\textbf{Roots the required roots are $\bf\dfrac{-5}{\sqrt{2}},\,-\sqrt{2}$}$