DISCUSS ■ DISCOVER: How Many Real Zeros Can a Polynomial Have? Give examples of polynomials that have thefollowing properties, or explain why it is impossible to findsuch 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, onlyone of which is rational(d) A polynomial of degree 4 that has four real zeros, noneof which is rationalWhat must be true about the degree of a polynomial withinteger coefficients if it has no real zeros?
DISCUSS ■ DISCOVER: How Many Real Zeros Can a Polynomial Have? Give examples of polynomials that have thefollowing properties, or explain why it is impossible to findsuch 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, onlyone of which is rational(d) A polynomial of degree 4 that has four real zeros, noneof which is rationalWhat must be true about the degree of a polynomial withinteger coefficients if it has no real zeros?
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.3: Dividing Polynomials
Problem 76E
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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?
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