Past Papers’ Solutions  Edexcel  AS & A level  Mathematics  Core Mathematics 1 (C16663/01)  Year 2013  June  Q#10
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Question
Given the simultaneous equation;
Where k is a non zerp constant.
a. Show that
Given that has equal roots,
b. find the value of K.
Solution
a.
We are given that;
To write a single equation in terms of x and k, we find expression for y from first equation;
We substitute this expression of y in second equation;
b.
We are given that;
We are given that given equation 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.
Since given is a quadratic equation with equal roots, its discriminant must be;
Now we have two options.









We are given that k is a nonzero constant, therefore, only option is;
c.
To solve the given simultaneous equations for , we can substitute this value of k in equation obtained in (a) to find x;
We substitute this value of x in the equation obtained in (a) for y as;
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