Question

For what values of p are the roots of the equation $4x^2+px+3=0$ real and equal? [CBSE 2014]

Answer 1

The given equation is $4x^2+px+3=0$.

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

$\therefore D=b^2-4ac=p^2-4\times 4\times 3=p^2-48$

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

$$\begin{gathered} \therefore p^2-48=0 \\ \Rightarrow p^2=48 \\ \Rightarrow p=\pm \sqrt{48}=\pm 4\sqrt{3} \end{gathered}$$

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