If a,b,c are in G.P. then the equations ${ax}^{2} + 2 bx + c = 0$ and ${dx}^{2} + 2 ex + ⨍ =0$ have a common root if d/a , e/b, f/c are in

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

H.P

G.P

A.P

A.G.P

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{l} G i v e n a, b, c a r e i n G . P \\ \Rightarrow b^{2} = a c \\ ∴ D i s c r i \min a n t o f a x^{2} + 2 b x + c = 0 i s \\ D = 4 b^{2} - 4 a c \Rightarrow 4 a c - 4 a c = 0 \\ ∴ T h e r o o t s a r e E q u a l \\ I f a x^{2} + 2 b x + c = 0 a n d d x^{2} + 2 c x + f = 0 \\ h a v e c o m m o n r o o t s w h i c h m e a n s \\ b o t h r o o t s o f t h e E q u a t i o n s a r e e q u a l \\ ∴ \frac{d}{a} = \frac{2 e}{2 b} = \frac{f}{c} \\ I f a, b, c a r e i n G . P t h e n d, e, f a r e a l s o i n G . P \\ ∴ \frac{d}{a}, \frac{e}{b}, \frac{f}{c} a r e i n G . P \end{array}$