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

The Biotic World is the best free Educational Website for Students. The Biotic World Provides NCERT Solution PDF, CBSE Notes PDF, NCERT Books PDF for class 8, 9, 10, 11, 12. The Biotic World also provides GU TDC Syllabus, Previous Years Question Papers, TDC notes on different topics of Physics, Chemistry, Mathematics, Zoology and Botany any many more. So, Follow us to get tuned with latest updates.

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
$\Rightarrow x^2+\frac{7x}{\sqrt{2}}+5=0$
$\Rightarrow x^2+(\sqrt{2}+\frac{5}{\sqrt{2}})x+5=0$
$\Rightarrow x^2+\sqrt{2}x+\frac{5}{\sqrt{2}}x+5=0$
$\Rightarrow x(x+\sqrt{2})+\frac{5}{\sqrt{2}}(x+\sqrt{2})=0$
$\Rightarrow (x+\sqrt{2})(x+\frac{5}{\sqrt{2}})=0$
$\Rightarrow x+\sqrt{2}=0, x+\frac{5}{\sqrt{2}}=0$
$\Rightarrow x=-\sqrt{2}, x=-\frac{5}{\sqrt{2}}$