Question

find the nature of the roots of the quadratic equation 4x square + 4 under root 3 X + 3 = 0​

Answer 1

since bsquare - 4ac = 0 the nature if the roots is real and equal

Answer 2

The nature of the roots are real and equal.

Step-by-step explanation:

Given : The quadratic equation $4x^2+4\sqrt{3}x+3=0$.

To find : The nature of the roots of the quadratic equation ?

Solution :

The nature of quadratic equation $ax^2+bx+c=0$ is determined by discriminant.

1) $D=b^2-4ac=0$ then roots are real and equal.

2) $D=b^2-4ac>0$ then roots are real and distinct.

3) $D=b^2-4ac<0$ then roots are imaginary.

In $4x^2+4\sqrt{3}x+3=0$, a=4, $b=4\sqrt{3}$ and c=3

Substitute in discriminant,

$D=b^2-4ac$

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

$D=48-48$

$D=0$

So, the roots are real and equal.

#Learn more

3x^2-2x-1 quadratic equation ​

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