Question

Obtain the roots of the following quadratic equation by using the general formula the solution:
$3x^2-2x+2=0$

Answer 1

We have the given equation

$3x^2-2x+2=0$

Here,

$a=3$

$b=-2$

$c=-2$

The formula for the roots of quadratic equation is $\frac{-b\pm {\left(b^2-4ac\right)}^{\frac{1}{2}}}{2a}$

now,

First root $x_1={\frac{-\left(-2\right)+\left[{\left(-2\right)}^2-4\times 3\times \left(-2\right)\right]}{2\times 3}}^{\frac{1}{2}}$

$=\frac{1+\sqrt{7}}{3}$

And, second roots $x_2={\frac{-\left(-2\right)-\left[{\left(-2\right)}^2-4\times 3\times \left(-2\right)\right]}{2\times 3}}^{\frac{1}{2}}$

$=\frac{1-\sqrt{7}}{3}$

Hence, $\frac{1+\sqrt{7}}{3},\frac{1-\sqrt{7}}{3}$ are the roots of given quadratic equation.