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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Answer:

Correct Answer: 28. (c)

Solution:

  1. 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} $



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