Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2004 | May-Jun | (P2-9709/02) | Q#3
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.
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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.
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Hence, there are following 03 solutions of ;
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