Question

If a, b, c are in G.P. and ax² + 2bx + c = 0 and px² + 2qx + r = 0 have common roots, then verify that pb² – 2qba + ra² = 0.

Answer 1

a, b, c are in G.P.

∴ b² = ac

ax² + 2bx + c = 0 becomes

have a common root, x = \(\frac{-\sqrt c}{\sqrt a}\) 

Satisfying px² + 2qx + r = 0