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

$4x^2+4\sqrt3x+3=0$

Given:

Given quadratic equation is $4x^2 + 4\sqrt3x + 3 = 0$.

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,

$a=4, b=4\sqrt3$ and $c=3$.

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

Therefore,

$D=(4\sqrt3)^2-4(4)(3)=16(3)-16(3)$

$=48-48$

$=0$

As $D=0$, the given quadratic equation has real and equal roots.

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Updated on: 10-Oct-2022

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