N1990 P1 Q1

The curve \(C\) has equation \(y = \frac{x^2 + 3x}{x - 1}\).

1. Find the exact set of values of \(y\) for which there are no point on \(C\).
2. Draw a sketch of \(C\), showing clearly any axis intercepts, asymptotes and turning points.
3. In the same diagram, draw a sketch of the curve \(y = (x - 5)^2 + 1\) and hence find the number of real roots of the equation \(x^3 - 12x^2 + 33x - 26 = 0\).