Question

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

• A. $\frac{1}{3}$
• B. 1
• C. 3
• D. $\frac{2}{3}$

Answer 1

The correct option is C 3

The quadratic equation is $3x^2+px+3=0$ and $p>0$

Let $a,b$ be two roots of quadratic equation

Given that $b=a^2$

We have $ab=a^3=\frac{3}{3}=1$

$\Rightarrow a=1,\omega ,{\omega }^2$

If $a=1$ , then $p$ will be negative

So take $a=\omega$

The sum of roots is $\omega +{\omega }^2=-1=-\frac{p}{3}$

$\Rightarrow p=3$

Therefore correct option is $C$