Question

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

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

On multiplying $\sqrt{2}$ with 5$\sqrt{2}$ we get 10.
We need a pair of numbers such that their sum gives 7 and product gives 10.

product : 2$\times$5 = 10 sum : 2+ 5 = 7

So the required pair is 2 and 5.

Now, $\sqrt{2}{x}^2+7x+5\sqrt{2}$

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

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

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

$\Rightarrow$ $\sqrt{2}$x + 5 = 0 or x + $\sqrt{2}$ = 0

i,e. x = $\frac{-5}{\sqrt{2}}$ or x = –$\sqrt{2}$

$\frac{-5}{\sqrt{2}}$ and – $\sqrt{2}$ are the roots of given quadratic equation.