∵α,β and γ are the roots of ax3+bx2+cx+d=0. and given β2=αγ i.e. α,β and γ are in G.P. So, ‌
α
K
,‌
β
K
and ‌
γ
K
are also in G.P. Now, u,v and w are roots of ak3x3+bk2x2+ckx+d‌‌=0 ‌ i.e. ‌‌‌a(kx)3+b(kx)2+c(kx)+d‌‌=0‌‌...(i) So, roots of Eq. (i) are ‌
α
K
,‌
β
K
and ‌
γ
K
i.e. u=‌
α
K
, v=‌
β
K
and w=‌
γ
K
From above, u,v and w are also in G.P. Hence, v2=uw.