If a, b, c are positive real numbers that are in G.P., then the equations ax2+2bx+c=0  and dx2+2ex+f=0have a common root if a/d , b/e , c/f are in

As b2=ac,ax2+2bx+c=0 can be written as ax2+2acx+c=0⇒(ax+c)2=0⇒x=−ca,−ca∴−ca is a root of dx2+2ex+f=0⇒dca−2eca+∫=0⇒da−2e1ac+fc=0⇒2eb=da+fc⇒da,eb,fc are in A.P.