The Root of the Problem

You are going to investigate quadratic equations where one root is related to the other. To begin you will look at equations of the form Use the applet below to help you answer the questions.

By varying the value of the slider k, what do you notice about x-intercepts of the quadratic graph? (Hint: it will be easier to notice the pattern if you choose integer values of k)

What is the connection between the value of k and the x-intercepts of the quadratic graph?

Write the quadratic equation in factorised form using the values of the x-intercepts in terms of k. Hint: if you know the x-intercepts of a quadratic are and you can write the quadratic in factorised form as as these are the x-vales which make the quadratic zero.

Expand this equation to find the values of the coefficients b and c in terms of k

Using what you have found and without solving the quadratic. Find the value of k and hence the x-intercepts of the graph with equation.