Quadratic Equations: Quadratic Formula

The Quadratic Formula. The quadratic equation


has the solutions

Consider the general quadratic equation

displaymath90

with tex2html_wrap_inline92 . First divide both sides of the equation by a to get

displaymath96

which leads to

displaymath98

Next complete the square by adding tex2html_wrap_inline100 to both sides

displaymath102

Finally we take the square root of both sides:

displaymath104

or

displaymath106

We call this result the Quadratic Formula and normally write it

displaymath108

Remark. The plus-minus sign states that you have two numbers tex2html_wrap_inline110 and tex2html_wrap_inline112 .

Example: Use the Quadratic Formula to solve

displaymath114

Solution. We have a=2, b= -3, and tex2html_wrap_inline11. By the quadratic formula, the solutions are

displaymath122

Please go to General Conclusion to find a summary of all the cases regarding the roots of a quadratic equation.

[Algebra] [Complex Variables]
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[Calculus] [Differential Equations] [Matrix Algebra]

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Author: Mohamed Amine Khamsi

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