Question

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

• A. $1/3$
• B. $1$
• C. $-6$
• D. $3$

Answer 1

Answer: (D)

$3$

Let $\alpha ,{\alpha }^2$ be the roots of $3x^2+px+3=0$

Now, $S=\alpha +{\alpha }^2=-\frac{p}{3},$

$P={\alpha }^3=1\Rightarrow \alpha =1,\omega ,{\omega }^2$

Now, $\alpha +{\alpha }^2=\frac{p}{3}$

$\Rightarrow \omega +{\omega }^2=-\frac{p}{3}\Rightarrow -1=-\frac{p}{3}\Rightarrow p=3$