**(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 and are such examples.

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Tue Jun 24 09:52:49 MDT 1997

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