Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$2 x^{2} + 5 \sqrt{3} x + 6 = 0$

Open in App

Solution

Roots are given by $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

$= \frac{- 5 \sqrt{3} \pm \sqrt{(5 \sqrt{3})^{2} - 4 \times 6 \times 2}}{2 \times 2}$

$= \frac{- 5 \sqrt{3} \pm \sqrt{75 - 48}}{4}$

$= \frac{- 5 \sqrt{3} \pm \sqrt{27}}{4}$

$= \frac{- 5 \sqrt{3} \pm 3 \sqrt{3}}{4}$

$= \frac{- \sqrt{3}}{2}, - 2 \sqrt{3}$

Suggest Corrections

Similar questions

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$x^{2} - 6 x + 4 = 0$

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$x^{2} + 5 x - (a^{2} + a - 6) = 0$

2 x^{2} + x - 4 = 0

2 x^{2} + a x - a^{2} = 0

x^{2} + 5 x - (a^{2} + a - 6) = 0

Join BYJU'S Learning Program