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  4. If the equations x2+2x+3=0 and ax2+bx+c=0, a, b, c ∈ R have a common root, then a: b: c is

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Q. If the equations $x^2+2x+3=0$ and $ax^2+bx+c=0, a, b, c \in R$ have a common root, then $a : b : c$ is

JEE MainJEE Main 2013Complex Numbers and Quadratic Equations

Solution:

Given equations are $x^2+2x+3=0 ...(i)$
and $ ax^2+bx+c=0 ...(ii)$
Since, Eq. (i) has imaginary roots, so Eq. (ii) will also
have both roots same as Eq. (i).
Thus,$ \frac{a}{1}=\frac{b}{2}=\frac{c}{3}$
Hence, $a : b : c$ is $1 : 2 : 3$.