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Tim Gan Math

1990 A-Level H2 Mathematics

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Question 1Graphing Techniques

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 \(x^3 - 12x^2 + 33x - 26 = 0\).
Solution step 1, image 1
Solution step 1, image 2
Solution step 2, image 1
Solution step 2, image 2
Solution step 3, image 1
Solution step 3, image 2
Solution step 3, image 3

Final Answer:

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