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If a, b, c are positive real numbers suc...

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

A

`1: 2: 3`

B

`3: 2: 1`

C

`1: 3 : 2`

D

`3 : 1 : 2 `

Text Solution

Verified by Experts

The correct Answer is:
1
` x^(2) + 2x + 3 = 0 `
` D = 2^(2) - 4 .1.3 lt 0 `
i.e., both roots are complex.
Hence , both roots are common of ` x^(2) + 2x + 3 = 0 `
and ` ax ^(2) + bx + c = 0`
`therefore (a)/(1) = (b)/(2) = (c)/(3)` .
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