Theory of Equations 1 Question 27
28. For the equation $3 x^{2}+p x+3=0, p>0$, if one of the root is square of the other, then $p$ is equal to
(2000, 1M)
(a) $1 / 3$
(b) 1
(c) 3
(d) $2 / 3$
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Solution:
- Let $\alpha, \alpha^{2}$ be the roots of $3 x^{2}+p x+3=0$
Now,
$$ \begin{aligned} & S=\alpha+\alpha^{2}=-p / 3 \\ & P=\alpha^{3}=1 \end{aligned} $$
$$ \Rightarrow \quad \alpha=1, \omega, \omega^{2} $$
Now, $\quad \alpha+\alpha^{2}=-p / 3$
$\Rightarrow \quad \omega+\omega^{2}=-p / 3$
$$ \begin{array}{rlrl} \Rightarrow & -1 & =-p / 3 \\ \Rightarrow & & p & =3 \end{array} $$
