For what values of p are the roots of the equation


For what values of $p$ are the roots of the equation $4 x^{2}+p x+3=0$ real and equal?



The given equation is $4 x^{2}+p x+3=0$.

This is of the form $a x^{2}+b x+c=0$, where $a=4, b=p$ and $c=3$.

$\therefore D=b^{2}-4 a c=p^{2}-4 \times 4 \times 3=p^{2}-48$

The given equation will have real and equal roots if D = 0.

$\therefore p^{2}-48=0$

$\Rightarrow p^{2}=48$

$\Rightarrow p=\pm \sqrt{48}=\pm 4 \sqrt{3}$

Hence, $4 \sqrt{3}$ and $-4 \sqrt{3}$ are the required values of $p$.


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