Question

Determine nature of roots of the quadratic equation $\sqrt{3}{x}^2+2\sqrt{3}x+\sqrt{3}=0$.
[2 Marks]

Answer 1

We know that the nature of roots of a quadratic equation, $a{x}^2+bx+c=0$ can be determined by observing the value of $b^2-4ac$.

Comparing $\sqrt{3}{x}^2+2\sqrt{3}x+\sqrt{3}=0$ with $a{x}^2+bx+c=0$

We get $a=\sqrt{3},b=2\sqrt{3},c=\sqrt{3}$

Now, $b^2-4ac=(2\sqrt{3}{)}^2-4(\sqrt{3}\left)\right(\sqrt{3})$

$=12-(4\times 3)$
$=12-12=0$

$b^2-4ac=0$
(1 Mark)

So, the roots of the given quadratic equation are real and equal.
(1 Mark)