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

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Solution

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

$a = 3, b = - 2, c = 2$

We know discriminant, $D = b^{2} - 4 a c$

$= (- 2)^{2} - 4 \times 3 \times 2$

$= 4 - 24 = - 20$

The discriminant is negative and so, there are no real roots for this equation.

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