Equation...pls help me!?

Question

We have 3mx^2+(2m + 1)*x + m+1=0,m is included in R and we have X1 and X2,the roots of the equation.Determine an independent relation from m (of m) between the roots X1 and X2. Hope u understood what I said here :)
Thank you!

Answer 1

x1+x2=-(2m+1)/3m
x1*x2= (m+1)/3m
m(3(x1+x2)+2)=-1 so m= -1/((3(x1+x2)+2))
m(3x1x2-1)=1 so m= 1/(3x1x2-1)
so
1-3*x1*x2=3(x1+x2)+2 independent of m

Answer 2

3mx^2+(2m + 1)*x + m+1=0,

x = [ -(2m+1) +or- sqrt( (2m+1)^2 - 4(3)(m+1) ) ] / 6m
= [ -2m - 1 +or- sqrt ( 4m^2 + 4m + 1 - 12m - 12) ] / 6m
= [ -2m -1 +or- sqrt( 4m^2 - 8m - 11) ] / 6m

x1 = [ -2m -1 + sqrt( 4m^2 - 8m - 11) ] / 6m
x2 = [ -2m -1 - sqrt( 4m^2 - 8m - 11) ] / 6m

This is how x1, x2 depends on m.