Question

Which of the following are the roots of 3 X square + 2 x minus 1 equal to 2

Answer 1

Answer:

Given equation

$3x ^{2} + 2x - 1 = 2$

is a quadratic equation in form of x.

Roots of given quadratic equation can be calculated as:-

$3 {x}^{2} + 2x - 1 = 2 \\ \\ 3 {x}^{2} + 2x - 3 = 0$

Using quadratic formula,

$x = \dfrac{ - 2 \pm \sqrt{ {2}^{2} - 4 \times 3 \times ( - 3)} }{2 \times 3} \\ \\ x = \dfrac{ -2 \pm \sqrt{4 + 48} }{6} \\ \\ x = \dfrac{ - 2 \pm \sqrt{52} }{6} \\ \\ x = \dfrac{ - 2 \pm2 \sqrt{13} }{6} \\ \\ x = \frac{ - 1 \pm \sqrt{13} }{3}$

So,

Roots of quadratic equation will be

$\frac{ - 1 + \sqrt{13} }{3} \\ and \\ \frac{ - 1 - \sqrt{13} }{3}$