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)(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.