If α,β are the roots of ax2+bx+c=0 and α+β,α2+β2,α3+β3 are in G.P., where △=b2−4ac, then
CONVENTIONAL APPROACH (α2+β2)2=(α+β)(α3+β3) (b2−2aca2)2=(−ba)(−b2+3abca3) ⇒4a2c2=acb2⇒ac(b2−4ac)=0 As a≠0⇒c△=0