TS EAMCET 6-Aug-2021 Shift 2 Question Paper

∵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.