Q. 43 explain why the facts given are ... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 4: Q. 43 (page 215)

explain why the facts given are contradictory.
f(x) is a polynomial function of degree 4 whose coefficients are real numbers; three of its zeros are 2, 1 + 2i, and 1 - 2i. Explain why the remaining zero must be a real number.

Short Answer

Expert verified

The fourth root should be a real one because if the fourth root is complex then its conjugate also becomes a root of the polynomial hence we have 5 roots and degree of polynomial becomes 5 which will be a contradiction

Step by step solution

Given information

We are given a statement

f(x) is a polynomial function of degree 4 whose coefficients are real numbers; three of its zeros are 2, 1 + 2i, and 1 - 2i. Explain why the remaining zero must be a real number.

Explanation

We are given that degree of polynomial is 4 and one root is 2 and other roots are 1+2i , 1-2i these are 3 roots the fourth root should be a real one because if the fourth root is complex then its conjugate also becomes a root of the polynomial hence we have 5 roots and degree of polynomial becomes 5 which will be a contradiction.

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91影视

explain why the facts given are contradictory.
f(x) is a polynomial function of degree 4 whose coefficients are real numbers; three of its zeros are 2, 1 + 2i, and 1 - 2i. Explain why the remaining zero must be a real number.

Short Answer

Step by step solution

Given information

Explanation

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91影视

explain why the facts given are contradictory.f(x) is a polynomial function of degree 4 whose coefficients are real numbers; three of its zeros are 2, 1 + 2i, and 1 - 2i. Explain why the remaining zero must be a real number.

Short Answer

Step by step solution

Given information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

explain why the facts given are contradictory.
f(x) is a polynomial function of degree 4 whose coefficients are real numbers; three of its zeros are 2, 1 + 2i, and 1 - 2i. Explain why the remaining zero must be a real number.