The curve $C$ has equation $y = \frac{x^2 + 3x}{x - 1}$. Find the exact set of values of $y$ f

Question

The curve $C$ has equation $y = \frac{x^2 + 3x}{x - 1}$. Find the exact set of values of $y$ for which there are no point on $C$. Draw a sketch of $C$, showing clearly any axis intercepts, asymptotes and turning points. 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 $x^3 - 12x^2 + 33x - 26 = 0$.

Accepted Answer

(i) $1< y <9$ (iii) $3$ real roots.

N1990 P1 Q1

N1990 P1 Q1

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