Polynomial Roots
Here, for any polynomial all real and complex zeros are calculated numerically and output as a table.
In addition, the polynomial is shown graphically with all its real zeros.
According to the fundamental theorem of algebra, an nth degree polynomial has a maximum of n real zeros.
If one also counts complex zeros, an nth degree polynomial has exactly n zeros (multiple zeros counted according to their multiplicity).
For quadratic, cubic and even quartic polynomials zeros can be calculated analytically. For polynomials of degree greater 4 this is in general possible only numerically.
An nth degree polynomial is defined here via its n + 1 coefficients. Coefficients can of course also be 0.
Alternatively, the polynomial can also be entered directly as the sum of powers of x (with ^ as the power operator).
For example, the following 2 alternatives are possible to define the same 5th degree polynomial:
x^5 - 8x^3 + 2x + 1 or 1 0 -8 0 2 1
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