Question

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 1

$\textbf{Given:}$

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

$\textbf{To find:}$

$\text{Roots of the given quadratic equation}$

$\textbf{Solution:}$

$\text{Consider,}$

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

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

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

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

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

$\implies\,x=\dfrac{-5}{\sqrt{2}}\;\text{(or)}\;x=-\sqrt{2}$

$\therefore\textbf{Roots the required roots are \bf\dfrac{-5}{\sqrt{2}},\,-\sqrt{2} }$

Answer 2

Answer:

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