p is a non-zero real number. If the equation whose roots are the squares of the roots ofthe equation x3−px2+px−1=0 is identical with the given equation, then p=
Let α,β,γ are roots of equation x3−px2+px−1=0 ∵α+β+γ‌‌=p αβ+βγ+αγ‌‌=p αβγ‌‌=1 ‌ Also given, ‌‌‌α2+β2+γ2‌‌=p α2β2+β2γ2+α2γ2‌‌=p α2β2γ2‌‌=1 ∴(α+β+γ)2=‌‌α2+β2+γ2+2(αβ+βγ+γα) p2=‌‌p+2p p2=‌‌3p p=3