# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2013 | June | Q#10

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 non-zero 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;