If b2=ac,equation ax2+2bx+c=0 and dx2+2ex+f=0
have common roots then da,eb,fc are in
A.P.
G.P.
H.P
Noneofthese
Explanation for the correct option:
Given,
ax2+2bx+c=0 and
b2=ac
x=[-2b±4b2-4ac]2a
=-ba
Now x=-ba is also roots of
dx2+2ex+f=0
⇒d-ba2+2e-ba+f=0
⇒2eba=db2a2+f
⇒ 2eb=dc+af
⇒ 2eb=da+fc
⇒da,(eb),(fc) are in AP
Hence option(A) is correct.
If a,b,c are in G.P, then the equation ax2 + 2bx + c = 0 and dx2 + 2ex + f = 0 have a common root if da,eb,fc are in