# 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

Hits: 67

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.  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 ;   