Question

If a, b and c are in GP, then the equations ax² +  2bx + c = 0 and dx² + 2ex + f  = 0 = have a common root. Show that d/a, e/b.f/c are in AP.

Answer 1

 Given a, b, and c are in GP. Now b² = ac. So ax² + 2bx  + c = 0 can be written as

This must be the common root by hypothesis. So it must 

satisfy the equation

Hence,  d/a,e/b,f/c are in AP.