MathsNet: A Level Pure 1 Module

P1 Topic 1: Proof
Proof 3: Roots of a quadratic equation
The interactive display below will show you each of the steps in the proof of the formula for the roots of a quadratic equation ax²+bx+c=0.

Note that this is not an easy proof to follow, so you may want to return to it later when you have studied more of your AS/A2 course.

There are eight steps in total.

Study each one in turn and see if you can follow how it was obtained from the line before. Move the mouse over the line itself and look at the status bar at the bottom to see a brief description of the step.

A few more notes on some of the steps
1	Dividing through by a: what if a was zero? The original equation would not be a quadratic one if a was zero, so we can safely assume a is not zero.
2	Completing the square: you will learn how to do this in the A Level course
5	Taking the square root: remember there is always a positive and a negative square root

Summary

Once you have understand the symbols, notation and language of mathematics, then you have to put it all together in a logical form. The concept of proof is central - and unique - to mathematics. Proof requires clear logical thinking. To help the clarity of your written work, pay attention to how you arrange things on the page. Work down the page rather than across. Use one line for each step. Line up things like "equals" or "implies" symbols as you work down the page so that the flow of the mathematics is as clear as possible.

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