prove that ax2+bx+c=0and x2+2x+c=0 cannot have a common root unless a:b:c=1:2:3

since bothe equations have common root

implies , take or assume your own root suppose "alpha" on substituting in the both equations the result that is the answer should remain the same in both the equations..

now comparing the coeff..in both the equations....

we get the answer..