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If the equation x^(2)+2x+3=0 and ax^(2)+...

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

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Given equations are
`ax^(2)+bx+c=0`…….i
and `x^(2)+2x+3=0`………..ii
Clearly, roots of Eq. (ii) are imaginary, since Eqs (i) and (ii) have a commoni root. Therefor, common root 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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