MAT 295 Lecture Notes - Lecture 5: Intermediate Value Theorem

• School: Syracuse University
• Department: Mathematics
• Course: MAT 295
• Professor: All

Document Summary

[a ,b] and let n be any number between f(a) and f(b) Then there is a number c between a and b with f(c)=n. **this theorem is only true when the graph is continuous. 4 =0 has a root (has y-value passing through 0) in. By the ivt, there has to be a c between 0 and 2 where f(c)=0. Theorem: if f is polynomial of odd degree, then f has a (real) root. Fundamental theorem of algebra: every nonconstant polynomial has a complex root.