Question

If the equations $x^2+2x+3=0$ and $a{x}^2+bx+c=0$, a, b, c $ϵ$ R, have a common root, then a: b: c is

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

Answer 1

The correct option is A 1: 2: 3

Given equations are
$x^2+2x+3=0...\left(i\right)$
$a{x}^2+bx+c=0...\left(ii\right)$
roots of equation (i) are imaginary roots.
According to the questions (ii) will also have both roots same as (i). Thus
$\frac{a}{1}=\frac{b}{2}=\frac{c}{3}=\lambda \left(say\right)\Rightarrow a=\lambda ,b=2\lambda ,c=3\lambda$
Hence, required ratio is 1:2:3