http://www.ck12.org Chapter 11. Complex Numbers
- 1, -3 (with multiplicity 3),− 1 ,
√
3 i,−√
3 i- 5 (with multiplicity 2), -1 (with multiplicity 2), 2i,− 2 i
4.i,−i,
√
2 i,−√
2 i
For each polynomial, factor into its linear factorization and state all of its roots.
5.f(x) =x^5 + 4 x^4 − 2 x^3 − 14 x^2 − 3 x− 18
6.g(x) =x^4 − 1
7.h(x) =x^6 − 12 x^5 + 61 x^4 − 204 x^3 + 532 x^2 − 864 x+ 576
8.j(x) =x^7 − 11 x^6 + 49 x^5 − 123 x^4 + 219 x^3 − 297 x^2 + 243 x− 81
9.k(x) =x^5 + 3 x^4 − 11 x^3 − 15 x^2 + 46 x− 24
10.m(x) =x^6 − 12 x^4 + 23 x^2 + 36
11.n(x) =x^6 − 3 x^5 − 10 x^4 − 32 x^3 − 81 x^2 − 85 x− 30
12.p(x) =x^6 + 4 x^5 + 7 x^4 + 12 x^3 − 16 x^2 − 112 x− 112
- How can you tell the number of roots that a polynomial has from its equation?
- Explain the meaning of the term “multiplicity”.
- A polynomial with real coefficients has one root that is
√
3 i. What other root(s) must the polynomial have?