Question

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

• A. –5/√2 and –√2
• B. 5/√2 and –√2
• C. 5/√2 and √2
• D. –5/√2 and √2

Answer 1

The correct option is A

–5/√2 and –√2

Multiply $\sqrt{2}$ with 5$\sqrt{2}$ and we get 10

Pairs whose product is 10 are

1$\times$10 = 10; sum 1+ 10 = 11

2$\times$5 = 10; sum 2+ 5 = 7

So our required pair is 2 and 5

$\sqrt{2}$ $x^2$ + 5x + 2x + 5\(\sqrt{2} = 0\)

$x$ ($\sqrt{2}x+5)$ + $\sqrt{2}$($\sqrt{2}x+5)=0$

($\sqrt{2}x+5\left)\right(x+\sqrt{2})=0$

$\sqrt{2}x+5=0$ and $x+\sqrt{2}=0$

$x=\frac{-5}{\sqrt{2}}$ and $x=–\sqrt{2}$

$\frac{-5}{\sqrt{2}}$ and – $\sqrt{2}$ are the roots.