Question

The roots of the following quadratic equation (if they exist) by the method of completing the square.
$2x^2$ + x - 4 = 0

are $\frac{\sqrt{33}-1}{4},\frac{-\sqrt{33}-1}{4}$

• A. True
• B. False

Answer 1

The correct option is A True

$2x^2+x-4=0$

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

$\Rightarrow$ Here, $a=1,b=\frac{1}{2},c=-2$

$\Rightarrow$ $x^2+\frac{x}{2}=2$

${\left(\frac{-b}{2a}\right)}^2={\left(\frac{-\frac{1}{2}}{2\left(1\right)}\right)}^2=\frac{1}{16}$

Adding $\frac{1}{16}$ on both sides,

$\Rightarrow$ $x^2+\frac{x}{2}+\frac{1}{16}=2+\frac{1}{16}$

$\Rightarrow$ ${(x+\frac{1}{4})}^2=\frac{33}{16}$

$\Rightarrow$ $x+\frac{1}{4}=\pm \frac{\sqrt{33}}{4}$

$\Rightarrow$ $x+\frac{1}{4}=\frac{\sqrt{33}}{4}$ and $x+\frac{1}{4}=-\frac{\sqrt{33}}{4}$

$\therefore$ $x=\frac{\sqrt{33}-1}{4}$ and $x=\frac{-\sqrt{33}-1}{4}$

$\Rightarrow$ Hence, we can see roots given in question are correct.