Consider the equation yx²+(y-1)x+(y-1)=0

1. Find the set values of y for which this equation has real roots.
2.Hence determine the range of the function

f(x)=(x+1)/(x²+x+1)

3. Explain why f(x) has no inverse.

Question

Consider the equation yx²+(y-1)x+(y-1)=0

1. Find the set values of y for which this equation has real roots.
2.Hence determine the range of the function 

f(x)=(x+1)/(x²+x+1)

3. Explain why f(x) has no inverse.

deoxna · Answer

I get that for the first question you can use the quadratic formula to get y in terms of x, and I get that there's a root at y=1. 

Wolfram alpha, however, says there is also an "integer root" at y=0. When you plugin y=0 to the negative equation you do get x=0.
But if you graph it there is no root at 0, so I am confused...