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If a, b, c are positive real numbers that are in G.P., then the equations and have a common root if are in
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a
A.P.
b
G.P.
c
H.P.
d
none of these
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Correct option is C
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.Similar Questions
If the roots of the equation,
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