Question

The roots of the following quadratic equation (if they exist) by the method of completing the square.
$4x^2+4\sqrt{3}x+3=0$

are $\frac{-\sqrt{3}}{2},\frac{-\sqrt{3}}{2}$

• A. True
• B. False

Answer 1

The correct option is A True

$4x^2+4\sqrt{3}x+3=0$

$x^2+\sqrt{3}x+\frac{3}{4}=0$

$\Rightarrow$ Here, $a=1,b=\sqrt{3},c=\frac{3}{4}$

$\Rightarrow$ $x^2+\sqrt{3}=-\frac{3}{4}$

${\left(\frac{-b}{2a}\right)}^2={\left(\frac{-\left(\sqrt{3}\right)}{2\left(1\right)}\right)}^2=\frac{3}{4}$

Adding $\frac{3}{4}$ on both sides,

$\Rightarrow$ $x^2+\sqrt{3}x+\frac{3}{4}=-\frac{3}{4}+\frac{3}{4}$

$\Rightarrow$ ${(x+\frac{\sqrt{3}}{2})}^2=0$

$\therefore$ $x+\frac{\sqrt{3}}{2}=0$ and $x+\frac{\sqrt{3}}{2}=0$

$\therefore$ $x=-\frac{\sqrt{3}}{2}$ and $x=-\frac{\sqrt{3}}{2}$

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