Given equations are x2+2x+3=0... (i) ax2+bx+c=0... (ii) Roots of equation (i) are imaginary roots in order pair. According to the question (ii) will also have both roots same as (i). Thus
a
1
=
b
2
=
c
3
=λ( say ) ⇒a=λ,b=2λ,c=3λ Hence, required ratio is 1: 2: 3