Question

Find the roots of the quadratic equation $\sqrt{2}{x}^2+7x+5\sqrt{2}=0$ using factorization method

• A. $\frac{5}{\sqrt{2}}$ and $-\sqrt{2}$
• B. $\frac{-5}{\sqrt{2}}$ and $-\sqrt{2}$
• C. $\frac{-5}{\sqrt{2}}$ and $\sqrt{2}$
• D. $\frac{5}{\sqrt{2}}$ and $\sqrt{2}$

Answer 1

The correct option is B

$\frac{-5}{\sqrt{2}}$ and $-\sqrt{2}$

Multiply $\sqrt{2}with5\sqrt{2}$ and we get 10
Pairs of 10 are
1*10 = 10 sum 1+ 10 = 11
2*5 = 10 sum 2+ 5 = 7
So our required pair is 2 and 5
$\sqrt{2}{x}^2+5x+2x+5\sqrt{2}=0$
$x(\sqrt{2}x+5)+\sqrt{2}(\sqrt{2}x+5)=0$
$(\sqrt{2}x+5)(x+\sqrt{2})=0$
$\sqrt{2}x+5=0$ and $x+\sqrt{2}=0$
$x=-\frac{-5}{\sqrt{2}}$ and $x=-\sqrt{2}$
$-\frac{5}{\sqrt{2}}$ and $-\sqrt{2}$ are our required roots of quadratic equation.