Given equation, x3−px2+qx−r=0 ...(i) Let α,β and γ are the roots of Eq. (i) Hence, α+β+γ=
−(−p)
1
=p ...(ii) αβ+βγ+γα=q ...(iii) αβγ=−(−r)=r ...(iv) Given that, two roots are equal and opposite in sign. Let α=−β From Eq. (ii), we get, α+β+γ=p −β+β+γ=p ⇒ γ=p ...(v) From Eq. (iv), we get, αβγ=r ⇒ −β2γ=r −β2p=r β2=
−r
p
...(vi) From Eq. (iii), we get αβ+βγ+γα=q −β2+βp+(−β)p=q ⇒