AP EAPCET 25-Aug-2021 Shift 2 Paper

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
⇒

r

p

+0=q
⇒ r = pq