Question

The roots of the quadratic equation $\sqrt{2}{x}^2-7x+5\sqrt{2}=0$ are

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

Answer 1

Answer: (A)

$\sqrt{2},\frac{5}{\sqrt{2}}$

Now,

$\sqrt{2}{x}^2-7x+5\sqrt{2}=0$

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

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

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

$\Rightarrow x=\sqrt{2},\frac{5}{\sqrt{2}}$.