Progression (Sequence and Series)Hard
Question
If a, b, c are in GP, then the equations ax2 + 2bx + c = 0 and dx2 + 2bx + f = 0 have a common root, if, 
are in
are inOptions
A.AP
B.GP
C.HP
D.None of these
Solution
Since a, b, c are in GP.
⇒ b2 = ac
Given, ax2 + abx + c = 0
⇒ ax2 + 2
x + c = 0
⇒ (√a x + √c)2 = 0
⇒
Since, ax2 + 2bx + c = 0 and dx2 + 2ex + f = 0 have common root.
∴ must satisfy dx2 + 2ex + f = 0
⇒
+ f = 0
⇒
= 0
⇒
(∵b2 = ac)
∴
are in AP.
⇒ b2 = ac
Given, ax2 + abx + c = 0
⇒ ax2 + 2
x + c = 0⇒ (√a x + √c)2 = 0
⇒
Since, ax2 + 2bx + c = 0 and dx2 + 2ex + f = 0 have common root.
∴
must satisfy dx2 + 2ex + f = 0⇒
+ f = 0⇒
= 0⇒
(∵b2 = ac)∴
are in AP.Create a free account to view solution
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