The Quadratic Formula. The quadratic equation

Consider the general quadratic equation
with . First divide both sides of the equation by a to get
which leads to
Next complete the square by adding to both sides
Finally we take the square root of both sides:
or
We call this result the Quadratic Formula and normally write it
Remark. The plusminus sign states that you have two numbers and .
Example: Use the Quadratic Formula to solve
Solution. We have a=2, b= 3, and . By the quadratic formula, the solutions are
Please go to General Conclusion to find a summary of all the cases regarding the roots of a quadratic equation.
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Author: Mohamed Amine Khamsi