Find the roots of \sqrt{2}x^2+7x+5\sqrt{2}=0 quadratic equations by factorization ?

byAmlesh Mahato •March 04, 2021

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Solution:

$Find the roots of \sqrt{2}x^2+7x+5\sqrt{2}=0 quadratic equations by factorization ?$
⇨ Divided by $\sqrt{2}$ on both side
$\Rightarrow x^2+\frac{7x}{\sqrt{2}}+5=0$
$\Rightarrow x^2+(\sqrt{2}+\frac{5}{\sqrt{2}})x+5=0$
$\Rightarrow x^2+\sqrt{2}x+\frac{5}{\sqrt{2}}x+5=0$
$\Rightarrow x(x+\sqrt{2})+\frac{5}{\sqrt{2}}(x+\sqrt{2})=0$
$\Rightarrow (x+\sqrt{2})(x+\frac{5}{\sqrt{2}})=0$
$\Rightarrow x+\sqrt{2}=0, x+\frac{5}{\sqrt{2}}=0$
$\Rightarrow x=-\sqrt{2}, x=-\frac{5}{\sqrt{2}}$