Pre-Calculus A, 4th Hour, Winter 2012: 2.5 The Fundamental Theorem of Algebra

Monday, January 23, 2012

The Fundamental Theorem of Algebra:

If $f(x)$ has a polynomial degree of $n$ , the number of zeros is also $n$

Conjugate Pairs:

$a+bi$ and $a-bi$

Finding a Polynomial with Given Zeros:

Example:

$x=2, -3, 4-i, 4+i$

$f(x)=(x-2)(x+3)(x-(4-i))(x-(4+i))$

$f(x)=(x-2)(x+3)(x-4+i)(x-4-i)$

$f(x)=(x^2+x-6)(x-4)^2-i^2$

$f(x)=(x^2+x-6)(x^2-8x+17)$

$f(x)=x^4-7x^3-15x^2+65x+102$