MathematicsFor the equation 5×2+px+5=0,p>0 if one root of the equation is square of the other, then p=

For the equation $5 x^{2} + p x + 5 = 0, p > 0$ if one root of the equation is square of the other, then $p =$

$α, α^{2}$ are the roots of $5 x^{2} + p x + 5 = 0$

$α + α^{2} = \frac{- p}{5}$ and $α . α^{2} = \frac{5}{5} = 1$

$\Rightarrow α^{3} = 1$

$\Rightarrow α = 1. ω, ω^{2}$

$1 + 1 = \frac{- p}{5}$

$\Rightarrow p = - 10$

$α = ω, ω + ω^{2} = \frac{- p}{5} \Rightarrow - 1 = \frac{- p}{5} \Rightarrow p = 5$

$α = ω^{2}, ω^{2} + ω^{4} = \frac{- p}{5} \Rightarrow ω^{2} + ω = \frac{- p}{5} \Rightarrow p = 5$

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