Question

Find the nature of the roots of the quadratic equation:

$13\sqrt{3}{x}^2+10x+\sqrt{3}=0$

Answer 1

Hint: find the discriminant of the given equation.

Concept Used: roots can be real, imaginary, equal, or unequal depending on the value of the discriminant. When $b^2-4ac<0$, then the roots are imaginary.

Calculating the discriminant of the given equation,

$\begin{array}{rcl}{b}^2-4ac& =& {10}^2-4\left(13\sqrt{3}\right)\sqrt{3}\\ & =& 100-4\left(39\right)\\ & =& 100-156\\ & =& -56<0\end{array}$

Hence, the roots of the equation are imaginary.