Question

Find the sum and the product of the roots of the equation $\sqrt{3}{x}^2+27x+5\sqrt{3}=0$.

Answer 1

Given:

$\sqrt{3}{x}^2+27x+5\sqrt{3}$

Here, $a=\sqrt{3}$, $b=27$, $c=5\sqrt{3}$

Sum of the roots $=\frac{-b}{a}=\frac{-27}{\sqrt{3}}=\frac{-9\times 3}{\sqrt{3}}=-9\sqrt{3}$

Product of the roots $=\frac{c}{a}=\frac{5\sqrt{3}}{\sqrt{3}}=5$