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Suppose a, b, c are real numbers, and ea...

Suppose a, b, c are real numbers, and each of the equations `x^(2)+2ax+b^(2)=0` and `x^(2)+2bx+c^(2)=0` has two distinct real roots. Then the equation `x^(2)+2cx+a^(2)=0` has - (A) Two distinct positive real roots (B) Two equal roots (C) One positive and one negative root (D) No real roots

A

Two distinct positive real roots

B

Two equal roots

C

One positive and one negative root

D

No real roots

Text Solution

Verified by Experts

The correct Answer is:
D
`x^(2)+2ax+b^(2)=0" "x^(2)+2bx+c^(2)=0`
`D_(1)gt0" "D_(2)gt0`
`4a^(2)+b^(2)gt0" "4b^(2)-4c^(2)gt0`
`a^(2)gtb^(2)…..(1)" "b^(2)gtc^(2)…….(2)`
From (1) and (2)
`a^(2)gtb^(2)gtc^(2)rArra^(2)gtc^(2)rArrc^(2)-a^(2)lt0`
`x^(2)+2cx+a^(2)=0`
`D=4c^(2)-4a^(2)lt0" No real roots"`
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Knowledge Check

  • If a, b, c are positive real numbers such that the equations ax^(2) + bx + c = 0 and bx^(2) + cx + a = 0 , have a common root, then

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