Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 2 (P29709/02)  Year 2004  MayJun  (P29709/02)  Q#3
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Question
The cubic polynomial is denoted by . It is given that is a factor of .
i. Find the value of .
ii. When has this value, solve the equation .
Solution
i.
We are given that;
We are also given that is a factor of .
When a polynomial, , is divided by , and is factor of , then the remainder is ZERO i.e. .
Therefore;
ii.
We are required to solve the equation;
We are given that;
Therefore;
We have found in (i) that , therefore;
We are also given that is a factor of .
When a polynomial, , is divided by , and is factor of , then the remainder is ZERO i.e. .
Therefore, division of with will yield a quadratic factor with ZERO remainder.
Therefore;
Hence;
Now we have two options.


One is a liner factor while other is quadratic factor and we need to solve both of them for .
First we solve linear factor.
Now we solve quadratic factor.
Standard form of quadratic equation is;
Solution of a quadratic equation is expressed as;
Now we have two options.






Hence, there are following 03 solutions of ;



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