Question

Find the roots of the equation $5x^2-6x-2=0$ by the method of completing the square.
[3 MARKS]

Answer 1

Concept : 1 Mark
Application : 2 Marks

We have, $5x^2-6x-2=0$

$\Rightarrow x^2-\frac{6}{5}x-\frac{2}{5}=0$

$\Rightarrow x^2-\frac{6}{5}x=\frac{2}{5}$ [Dividing throughout by 5]

$\Rightarrow x^2-2\left(\frac{3}{5}\right)x+{\left(\frac{3}{5}\right)}^2=\frac{2}{5}+{\left(\frac{3}{5}\right)}^2$

[Adding ${\left(\frac{b}{2a}\right)}^2$ on both sides]

$\Rightarrow {(x-\frac{3}{5})}^2=\frac{19}{25}$

$\Rightarrow x-\frac{3}{5}=\pm \frac{\sqrt{19}}{5}$

$\Rightarrow x=\frac{3}{5}\pm \frac{\sqrt{19}}{5}=\frac{3\pm \sqrt{19}}{5}$

$\Rightarrow x=\frac{3+\sqrt{19}}{5}or,x=\frac{3-\sqrt{19}}{5}$

Hence, the roots of the given equation are $\frac{3+\sqrt{19}}{5}$ and $\frac{3-\sqrt{19}}{5}$