Past Papers’ Solutions  Edexcel  AS & A level  Mathematics  Core Mathematics 1 (C16663/01)  Year 2006  June  Q#8
Hits: 23
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.
Comments