Question

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

• A. $-9\sqrt{3},5$
• B. $9\sqrt{3},5$
• C. $6\sqrt{3},-5$
• D. $6\sqrt{3},5$

Answer 1

Answer: (A)

$-9\sqrt{3},5$

$Formulaused$
$sumofroot=\frac{-b}{a}$
$productofroots=\frac{c}{a}$
$Given$
$\sqrt{3}{x}^2+27x+5\sqrt{3}=0$
$comparingwitha{x}^2+bx+c=0$
$a=\sqrt{3},b=27,c=5\sqrt{3}$
$sumofroots=\frac{-27}{\sqrt{3}}$
$=\frac{-27}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}$
$=\frac{-27\sqrt{3}}{3}$
$=-9\sqrt{3}$
$productofroots=\frac{5\sqrt{3}}{\sqrt{3}}$
$=5$