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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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