If `a ,b ,c in R` and equations `a x^2+b x+c=0a n dx^2+2x+9=0` have a common a rot, then find `a : b : cdot`

Answer

`1:2:9`

Explanation

Given equation are
`x^(2) + 2x + 9 = 0` (1)
and `ax^(2) + bx + c = 0 ` (2)
Clearly, roots of Eq. (1) are imaginary . Eqs (1) and (2) have a
common root which must be imaginary, hance, both the roots will
common.Thereofore, Eqs (1) and (2) are identical
`therefore (a)/(1) = (b)/(2) = (c)/(9) or a : b:c = 1: 2 : 9` .