# Roots of a quadratic equation

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Derive the generic formula for the roots of a quadratic equation including conditions for which the there are two distinct real roots, one real and equal root and complex/unreal roots. Examples of each are presented.

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##### Solution Summary

This shows how to derive the formula for roots of a quadratic equation for specific situations. The equal roots and complex/unreal roots are analyzed.

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Please refer to the attached Microsoft Word Document.

Roots of a Quadratic Equation (with examples)

1. A quadratic equation can be represented by the following:

where , , and are rational and is not zero

2. The roots of this quadratic equation can be determined as follows:

(0.1)

divide (0.1) by gives:

(0.2)

subtracting from both sides of (0.2) gives:

i.e.:

(0.3)

Now to solve this, we need to complete the square for the expression on the left hand side of (0.3) i.e.

To do this, we apply the rule for completing a square which is to add the square of half the coefficient of ...

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