9.9 The Fundamental Theorem of Algebra

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9.9 The Fundamental Theorem of Algebra

The Fundamental Theorem of Algebra
Every polynomial equation with complex coefficients and positive degree n has exactly n complex roots. You may have to count the same number more than once if it is a root. double

Theorem: If a polynomial equation with real coefficients has
Theorem: If a polynomial equation with real coefficients has as a root (a and b real), then is also a root. In other words, imaginary roots come in pairs Just like we did with quadratic equations, we can also write the equation of any polynomial from its roots. complex conjugates

Find the polynomial equation of least degree having the given roots.
1. 2, 1, -4

Find the polynomial equation of least degree having the given roots.
2. 2, 1,

Given the following root(s) for the polynomial equation, find the remaining roots.
3.

Given the following root(s) for the polynomial equation, find the remaining roots.
4.

Given the following root(s) for the polynomial equation, find the remaining roots.
5.

Given the following root(s) for the polynomial equation, find the remaining roots.
6.