The correct options are
B a, b, c are in G.P.
E (x−α) is a factor of ax2+2bx+c.
Operating R3−(αR1+R2) and expanding, we shall easily get Δ=−(aα2+2bα+c)(ac−b2).
Hence Δ is zero if ac−b2=0
or aα2+2bα+c=0, i.e., a, b, c
are in G.P. or x−α is a factor of ax2+2bx+c