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 $3x^2+px+3=0$
Now, $S=\alpha +{\alpha }^2=-p/3$
$P={\alpha }^3=1\Rightarrow \alpha =1,\omega ,{\omega }^2$
Now, $\alpha +{\alpha }^2=-p/3$
$\Rightarrow \omega +{\omega }^2=-p/3$
$\Rightarrow -1=-p/3\Rightarrow p=3$