Solve the following quadratic equation by factorization:

$\sqrt{2}x^2-3x-2\sqrt2=0$

Given:

Given quadratic equation is $\sqrt{2}x^2-3x-2\sqrt2=0$.

To do:

We have to solve the given quadratic equation.

Solution:

$\sqrt{2}x^2-3x-2\sqrt2=0$

To factorise $\sqrt{2}x^2-3x-2\sqrt2=0$, we have to find two numbers $m$ and $n$ such that $m+n=-3$ and $mn=\sqrt{2}\times(-2\sqrt{2})=-2(\sqrt2)^2=-4$.

If $m=-4$ and $n=1$, $m+n=-4+1=-3$ and $mn=(-4)1=-4$.

$\sqrt{2}x^2-4x+x-2\sqrt2=0$

$\sqrt{2}x(x-2\sqrt2)+1(x-2\sqrt2)=0$

$(\sqrt{2}x+1)(x-2\sqrt2)=0$

$\sqrt{2}x+1=0$ or $x-2\sqrt2=0$

$\sqrt{2}x=-1$ or $x=2\sqrt2$

$x=\frac{-1}{\sqrt2}$ or $x=2\sqrt2$

$x=-\frac{1}{\sqrt2}$ or $x=2\sqrt2$

The values of $x$ are $-\frac{1}{\sqrt2}$ and $2\sqrt2$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

44 Views

Kickstart Your Career

Get certified by completing the course

Get Started