Question

For the equation $3x^2+px+3=0,p>0,$ if one of the root is square of the other, then $p$ is equal to

• A. 1/3
• B. 1
• C. 3
• D. 2/3

Answer 1

Answer: (C)

Let, $\alpha, \alpha^{2}$ be the roots of $3 x^{2}+p x+3=0$
Now, $S=\alpha+\alpha^{2}=-p / 3$
$P=\alpha^{3}=1 \Rightarrow \alpha=1, \omega, \omega^{2}$
Now, $\alpha+\alpha^{2}=-p / 3$
$\Rightarrow \omega+\omega^{2}=-p / 3$
$\Rightarrow-1=-p / 3 \Rightarrow p=3$