Exercise 6.

(a) Show that every polynomial of degree 3 has at least one x-intercept.

(b) Give an example of a polynomial of degree 4 without any x-intercepts.

Answer.

(a) Since complex roots show up in pairs, not all 3 roots can be complex, so at least one of them must be real! Or: Go back to your solution of Exercise 5. Every case has at least one real root.

(b) Now it can happen that all roots are complex! The polynomials tex2html_wrap_inline31 and tex2html_wrap_inline33 are such examples.

[Back] [Exercises] [Next]
[Algebra] [Trigonometry] [Complex Variables]
[Calculus] [Differential Equations] [Matrix Algebra]

S.O.S MATHematics home page

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

Helmut Knaust
Tue Jun 24 09:52:49 MDT 1997

Copyright 1999-2017 MathMedics, LLC. All rights reserved.
Contact us
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour