In the following, determine whether the given quadratic equations have real roots and if so, find the roots:

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

Given:

Given quadratic equation is $3x^2-2x+2=0$.

To do:

We have to determine whether the given quadratic equation has real roots.

Solution:

Comparing the given quadratic equation with the standard form of the quadratic equation $ax^2+bx+c=0$, we get,

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

The discriminant of the standard form of the quadratic equation $ax^2+bx+c=0$ is

$D=b^2-4ac$.

Therefore,

$D=(-2)^2-4(3)(2)=4-24=-20$.

As $D<0$, the given quadratic equation has no real roots. 

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Updated on: 10-Oct-2022

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