Term
| What are the objectives of precalculus 3.5? |
|
Definition
-Learn The Basic Facts About The Complex Zeros of Polynomials
-Use the conjugate pairs theorem to find the zeros of a polynomial |
|
|
Term
| The conjugate of a complex number z=a+bi is |
|
Definition
|
|
Term
| If z=a+bi is a zero of P, then... |
|
Definition
_
z=a-bi is also a zero of P |
|
|
Term
| Every polynomial with a complex coefficient has at least one... |
|
Definition
|
|
Term
| If p(x) is a polynomial of degree n is greater than or equal to one, it can be factored at n, linear factors of the form: |
|
Definition
| p(x)=(x-r)(x-rsubscrpt2) (x-rsubscrptn) |
|
|
Term
Find the polynomial with roots:
{1,-1,-i,i}
A Leading Coefficient of 1
A Degree of 4 |
|
Definition
p(x)=(x-1)(x+1)(x-i)(x+i)
(x^2-1) (x^2+1)
x^4-1 |
|
|
Term
| When finding a polynomial using roots a leading coefficient, and degree... |
|
Definition
1.) Use the roots and leading coefficient given and write a polynomial in
p(x)=(x-r)(x-rsubscrpt2) (x-rsubscrptn)
2.) Expand upon that polynomial until you get an answer with the proper degree |
|
|
Term
Find the factored form of the polynomial with a degree of 6, and roots {1,-1,2+i,1-sqrt2}
With Leading Coefficient 1 |
|
Definition
(x-1)(x+1)(x-1-sqrt2)(x-1+sqrt2)(x-2-i)
(x-2+i) |
|
|
Term
| Odd Degree Polynomials have.. |
|
Definition
|
|
Term
| How to find all zeros of a polynomial and graph |
|
Definition
1.) Find the Degree
2.) Find all possible rational zeros
-2a.) Find the Factors of the Last Number In the Polynomial
-2b.) Find the Factors of the Leading Coefficient
-3c.) Pair off the factors of both and divide them to determine the rational zeros of the polynomial
3.) Find the number of positive and negative zeros
-3a.) The number of variations of sign minus any even non-negative integer
[f(x)] = Number of Positive Zeros
-3b.) The number of variations of sign minus any even non-negative integer
[f(-x)] the number of negative zeros |
|
|
