Quadratic Equations: Quadratic Formula .how to derive the general formular /almighty formular

The Quadratic Formula. The quadratic equation

has the solutions
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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.

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