Determine the nature of the roots of the following quadratic equations:

$2x^2 - 6x + 3 = 0$

Given:

Given quadratic equation is $2x^2 - 6x + 3 = 0$.

To do:

We have to determine the nature of the roots of the given quadratic equation.

Solution:

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

$a=2, b=-6$ and $c=3$.

The discriminant of the standard form of the quadratic equation $ax^2+bx+c=0$ is $D=b^2-4ac$.

Therefore,

$D=(-6)^2-4(2)(3)=36-24=12>0$.

As $D>0$, the given quadratic equation has real and distinct roots.

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Updated on: 10-Oct-2022

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