Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2006 | June | Q#8

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Question

The equation , where p is a positive constant, has equal roots.

a.   Find the value of p.

b.   For this value of p, solve the equation .

Solution

a.
 

We are given the equation;

It is evident that it is a quadratic equation. 

We also given that it has equal roots.

For a quadratic equation , the expression for solution is;

Where  is called discriminant.

If , the equation will have two distinct roots.

If , the equation will have two identical/repeated roots.

If , the equation will have no roots.

Therefore, for the given equation;

Now we have two options.

We are given that p is a positive constant, therefore, .

 

b.    

 

We are required to solve the equation;

We have found in (a) that . Therefore;

Now we have two options.

It turned out the same as was given that given equation had equal roots.

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