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.© BrainMass Inc. brainmass.com December 24, 2021, 4:44 pm ad1c9bdddf
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:
divide (0.1) by gives:
subtracting from both sides of (0.2) gives:
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 ...
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.