First slide

Theory of equations

Question

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

Moderate

Solution

$α + α^{2} = - \frac{p}{3} and α . α^{2} = 1 .$
So $α = 1, ω, ω^{2} .$ If $α = 1, p < 0$ .
If $α = ω or ω^{2}$ , we have $ω + ω^{2} = - \frac{p}{3}$ .

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