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If equations ax^(2)-bx+c=0 (where a,b,c ...

If equations `ax^(2)-bx+c=0` (where `a,b,c epsilonR` and `a!=0`) and `x^(2)+2x+3=0` have a common root, then show that `a:b:c=1:2:3`

Text Solution

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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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