Question

If a, b, c are in G.P. then the equations ax² + 2bx + c = 0, dx² + 2ex + f = 0 have a common roots if are in

• A. A.P.
• B. G.P.
• C. H.P.
• D. None of these

Answer 1

Answer: (A)

A.P.

Answer 2

We have b² = ac …..(1)

For ax² + 2bx + c = 0 ̃ D = 4b² – 4ac = 0 by (1)

\ Roots of ax² + 2bx + c = 0 are equal.

hence if root is a then

a + a = – ̃ a = – …(2)

this a is also a root of dx² + 2ex + f = 0

\ d. + 2e + f = 0

̃ = 0 ̃ = 0 Q b² = ac

̃ ̃ henceare in A.P.