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]

Question

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]

Smart Achievers · Accepted Answer

(3)

$Let α, α^{2} be the roots of 3 x^{2} + p x + 3 = 0$

$∴$ $α + α^{2} = - \frac{p}{3} and α^{3} = 1$

$\Rightarrow (α - 1) (α^{2} + α + 1) = 0$ $\Rightarrow α = 1 or α^{2} + α = - 1$

$If α = 1, then p = - 6, which is not possible as p > 0$

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

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