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 $x^2+2x+3=0$ ......(i)
And $a{x}^2+bx+c=0$ ....(ii)
Since, Eq. (i) has imaginary roots, so Eq. (ii) will also have both roots same as Eq. (i), (because imaginary roots always occur in pair. If one root is a+ib, then other is a-ib.)
Thus, $\frac{a}{1}=\frac{b}{2}=\frac{c}{3}$
Hence, a : b : c is 1 : 2 : 3