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Option 1 : cr2 + (2c – b2)r + c = 0
Let the roots which are in geometric progression be a and ar
here, r is called as common ratio
⇒ a + ar = - b (sum of roots = -b)
⇒ a(1 + r) = - b
⇒ a = -b/(1 + r)
⇒ a × ar = c ( product of roots = c)
⇒ a2r = c
⇒ (- b/(1 + r))2 r = c
⇒ b2r = c + cr2 + 2cr
⇒ cr2 + (2c – b2)r + c = 0
∴ option 1 is correct
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