Question

Comment on the nature of the roots of the Quadratic equation $3\sqrt{3}{x}^2+10x+\sqrt{3}=0$.

Answer 1

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

Here, $a=3\sqrt{3},b=10,c=\sqrt{3}$

$△=b^2-4ac=100-4\left(3\sqrt{3}\right)\left(\sqrt{3}\right)=100-36=64\ge 0$

$\therefore △\ge 0$

Hence, roots are real and distinct.