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.


(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.

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

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