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

Options

A. `3:2:1`
B. `1:3:2`
C. `3:1:2`
D. `1:2:3`

Answer

C

Explanation

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`