DISCUSS DISCOVER: How Many Real Zeros Can a Polynomial Have? Give examples of polynomials that have the following properties, or explain why it is impossible to find
such a polynomial.
(a) A polynomial of degree 3 that has no real zeros
(b) A polynomial of degree 4 that has no real zeros
(c) A polynomial of degree 3 that has three real zeros, only
one of which is rational
(d) A polynomial of degree 4 that has four real zeros, none
of which is rational
What must be true about the degree of a polynomial with
integer coefficients if it has no real zeros?