Quadratic Equation

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Some caution is advised in using this solution. When b is much, much larger than a and c, the usual formula loses several places of accuracy. A better solution is:

$x_1=-\left(\frac{b+\text{sgn}(b)sqrt{b^2-4ac}}{2a}\right)$ $x_2=\frac{c}{ax_1}$

Numerical analysis can be a very difficult topic.

The general quadratic equation has the form $ax^2+bx+c=0.$

The general solution is given by:


A similar, but much more complex solution is possible for the cubic equation; and an even worse one for the quartic equation. Beyond that (quintic equation and higher) no such solution exists.

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