Question

Find the roots of the following quadratic equations by the factorization method.
$3\sqrt{2}{x}^2-5x-\sqrt{2}=0$

Answer 1

Given equation is $3\sqrt{2}{x}^2-5x-\sqrt{2}=0$
$3\sqrt{2}{x}^2-(6x-x)-\sqrt{2}=0$ [by splitting the middle term]
$3\sqrt{2}{x}^2-6x+x-\sqrt{2}=0$
$3\sqrt{2}{x}^2-3\sqrt{2}\sqrt{2}x+x-\sqrt{2}=0$
$\Rightarrow 3\sqrt{2}x(x-\sqrt{2})+1(x-\sqrt{2})=0$
$\Rightarrow (x-\sqrt{2})(3\sqrt{2}x+1)=0$
$Now,x-\sqrt{2}=0\Rightarrow x=\sqrt{2}$
$and3\sqrt{2}x+1=0$
$\Rightarrow x=\frac{-1}{3\sqrt{2}}=\frac{-\sqrt{2}}{6}$
Hence, the roots of the equation $3\sqrt{2}{x}^2-5x-\sqrt{2}=0are-\frac{\sqrt{2}}{6}and\sqrt{2}$