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If the equation x^2+2x+3=0 and ax^2+bx+c...

If the equation `x^2+2x+3=0` and `ax^2+bx+c=0` have a common root then `a:b:c` is

A

`3:2:1`

B

`1:3:2`

C

`3:1:2`

D

`1:2:3`

Text Solution

Verified by Experts

The correct Answer is:
C
Given equations are
`ax^(2)+bx+c=0`………….i
and `x^(2)+2x+3=0`…………ii
Clearly, roots of Eq. (ii) are imaginary, sicne Eqs I and ii have a common root, therefore common roots must be imaginary and hence both roots will be common. Therefore, Eqs i and ii are identical.
`:.a/1=b/2=c/3` or `a:b:c=1:2:3`
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