The most general methods which will cope with any quadratic equation in one variable are: The quadratic formula. Completing the square. Whether the roots are integers, rational, irrational, or even non-Real Complex numbers, both methods can both locate them. Quadratic formula The roots of are given by the formula:
Completing the square Given:
We can now rewrite our equation as follows:
Dividing both sides by a we find:
Which can be simplified to:
So the quadratic formula and completing the square are somewhat equivalent, however in some situations completing the square can be a little cleaner: For example, factoring by completing the square:
You may also use the quadratic formula: is with , , thus has zeros:
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