Question

If a, b, c are in G.P., then the equations ax² + 2bx+c = 0 and dx? +2ex + f = 0 have a common root
d e f
if -,-,-are in -
a b c
please answer my question​

Answer 1

Answer:

a, B, C are in G. P

b^2=ac

now the eq ax^2 + 2bx +C can be written as ax^2+2√acx +C =0

=> (√ax +√c)^2=0 => x=-√(c/a), -√(c/a)

if the two eq have equal roots, then it must be -√c/a

d(c/a) -2e√(c/a) +f=0

d/a, e/b, f/c are in A. P