Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 2 (P29709/02)  Year 2003  MayJun  (P29709/02)  Q#2
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Question
The polynomial is denoted by .
i. Find the value of the constant for which
ii. Hence solve the equation , giving your answers in an exact form.
Solution
i.
We are given that;
We are also given that;
We equate the two equations.
We can expand the R.H.S.
Comparing terms on both sides of the equation;
Since we are looking for value of constant and there are two equations containing constant ;








Hence;
ii.
We are required to solve the equation;
We are given that;
Therefore;
We are also given that;
We have found in (i) that ; therefore;
Hence;
Now we have two options.


These are both quadratic equations and we need to solve them for .
Standard form of quadratic equation is;
Solution of a quadratic equation is expressed as;
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