Question

The value of $k$, for which the quadratic equation $4x^2+4\sqrt{3}x+k=0$ has equal roots is :

• A. $k=2$
• B. $k=-2$
• C. $k=-3$
• D. $k=3$

Answer 1

The correct option is D $k=3$

Given: Quadratic equation $4x^2+4\sqrt{3}x+k=0$, has equal roots

A quadratic equation has equal roots if the discriminant, $D=b^2-4ac=0$

In the given equation, $a=4,b=4\sqrt{3},c=k$

Therefore the discriminant is $(4\sqrt{3}{)}^2-4(4\left)\right(k)=0$

$48-16k=0⟹16k=48$

Therefore, $k=3$