If the equations x2+2x+3=0 and ax2+bx+c=0 , a , b , c ^I R , have a common root, then a: b: c is
1:2:3
x2+2x+3=0 ....... (i)
ax2+bx+c=0 ......... (ii)
Since equation (i) has imaginary roots
So equation (ii) will also have both roots same as (i) , Thus
a1=b2=c3 ⇒ a=λ,b=2λ,c=3λ
Hence 1:2:3