Algebra and Trigonometry: Structure and Method, Book 2
Algebra and Trigonometry: Structure and Method, Book 2
2000th Edition
ISBN: 9780395977255
Author: MCDOUGAL LITTEL
Publisher: McDougal Littell
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Chapter 8.7, Problem 16OE
To determine

To state: that equation have no rational roots.

Expert Solution & Answer
Check Mark

Answer to Problem 16OE

None of the possible roots satisfy the equation so the equation have no rational roots.

Explanation of Solution

Given information:

The equation is x3+3x3=0 .

the possible rational roots of equation can be given by:

  rational roots=constant termcoffiecient of highest degree rational roots=31

Thus, the possible rational roots are ±1,±3 .

Now, use synthetic division,

    11033
    114
    1141
    11033
    114
    1147
    31033
    3936
    131233
    31033
    3936
    131239

Thus, none of the possible rational roots satisfy the equation.

Thus, the equation have no rational roots.

Chapter 8 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 8.1 - Prob. 11OECh. 8.1 - Prob. 12OECh. 8.1 - Prob. 1WECh. 8.1 - Prob. 2WECh. 8.1 - Prob. 3WECh. 8.1 - Prob. 4WECh. 8.1 - Prob. 5WECh. 8.1 - Prob. 6WECh. 8.1 - Prob. 7WECh. 8.1 - Prob. 8WECh. 8.1 - Prob. 9WECh. 8.1 - Prob. 10WECh. 8.1 - Prob. 11WECh. 8.1 - Prob. 12WECh. 8.1 - Prob. 13WECh. 8.1 - Prob. 14WECh. 8.1 - Prob. 15WECh. 8.1 - Prob. 16WECh. 8.1 - Prob. 17WECh. 8.1 - Prob. 18WECh. 8.1 - Prob. 19WECh. 8.1 - Prob. 20WECh. 8.1 - Prob. 21WECh. 8.1 - Prob. 22WECh. 8.1 - Prob. 23WECh. 8.1 - Prob. 24WECh. 8.1 - Prob. 25WECh. 8.1 - Prob. 1PCh. 8.1 - Prob. 2PCh. 8.1 - Prob. 3PCh. 8.1 - Prob. 4PCh. 8.1 - Prob. 5PCh. 8.1 - Prob. 6PCh. 8.1 - Prob. 7PCh. 8.1 - Prob. 8PCh. 8.1 - Prob. 9PCh. 8.1 - Prob. 10PCh. 8.1 - Prob. 11PCh. 8.1 - Prob. 12PCh. 8.1 - Prob. 13PCh. 8.1 - Prob. 14PCh. 8.1 - Prob. 15PCh. 8.1 - Prob. 16PCh. 8.1 - Prob. 17PCh. 8.1 - Prob. 18PCh. 8.1 - Prob. 19PCh. 8.1 - Prob. 20PCh. 8.1 - Prob. 1MRECh. 8.1 - Prob. 2MRECh. 8.1 - Prob. 3MRECh. 8.1 - Prob. 4MRECh. 8.1 - Prob. 5MRECh. 8.1 - Prob. 6MRECh. 8.1 - Prob. 7MRECh. 8.1 - Prob. 8MRECh. 8.1 - Prob. 9MRECh. 8.2 - Prob. 1OECh. 8.2 - Prob. 2OECh. 8.2 - Prob. 3OECh. 8.2 - Prob. 4OECh. 8.2 - Prob. 5OECh. 8.2 - Prob. 6OECh. 8.2 - Prob. 7OECh. 8.2 - Prob. 8OECh. 8.2 - Prob. 9OECh. 8.2 - Prob. 10OECh. 8.2 - Prob. 11OECh. 8.2 - Prob. 12OECh. 8.2 - Prob. 13OECh. 8.2 - Prob. 14OECh. 8.2 - Prob. 1WECh. 8.2 - Prob. 2WECh. 8.2 - Prob. 3WECh. 8.2 - Prob. 4WECh. 8.2 - Prob. 5WECh. 8.2 - Prob. 6WECh. 8.2 - Prob. 7WECh. 8.2 - Prob. 8WECh. 8.2 - Prob. 9WECh. 8.2 - Prob. 10WECh. 8.2 - Prob. 1PCh. 8.2 - Prob. 2PCh. 8.2 - Prob. 3PCh. 8.2 - Prob. 4PCh. 8.2 - Prob. 5PCh. 8.2 - Prob. 6PCh. 8.2 - Prob. 7PCh. 8.2 - Prob. 8PCh. 8.2 - Prob. 9PCh. 8.2 - Prob. 10PCh. 8.2 - Prob. 11PCh. 8.2 - Prob. 12PCh. 8.2 - Prob. 13PCh. 8.2 - Prob. 14PCh. 8.2 - Prob. 1STCh. 8.2 - Prob. 2STCh. 8.2 - Prob. 3STCh. 8.2 - Prob. 4STCh. 8.2 - Prob. 5STCh. 8.2 - Prob. 6STCh. 8.2 - Prob. 7STCh. 8.3 - Prob. 1OECh. 8.3 - Prob. 2OECh. 8.3 - Prob. 3OECh. 8.3 - Prob. 4OECh. 8.3 - Prob. 5OECh. 8.3 - Prob. 6OECh. 8.3 - Prob. 7OECh. 8.3 - Prob. 8OECh. 8.3 - Prob. 9OECh. 8.3 - Prob. 10OECh. 8.3 - Prob. 11OECh. 8.3 - Prob. 12OECh. 8.3 - Prob. 1WECh. 8.3 - Prob. 2WECh. 8.3 - Prob. 3WECh. 8.3 - Prob. 4WECh. 8.3 - Prob. 5WECh. 8.3 - Prob. 6WECh. 8.3 - Prob. 7WECh. 8.3 - Prob. 8WECh. 8.3 - Prob. 9WECh. 8.3 - Prob. 10WECh. 8.3 - Prob. 11WECh. 8.3 - Prob. 12WECh. 8.3 - Prob. 13WECh. 8.3 - Prob. 14WECh. 8.3 - Prob. 15WECh. 8.3 - Prob. 16WECh. 8.3 - Prob. 17WECh. 8.3 - Prob. 18WECh. 8.3 - Prob. 19WECh. 8.3 - Prob. 20WECh. 8.3 - Prob. 21WECh. 8.3 - Prob. 22WECh. 8.3 - Prob. 23WECh. 8.3 - Prob. 24WECh. 8.3 - Prob. 25WECh. 8.3 - Prob. 26WECh. 8.3 - Prob. 27WECh. 8.3 - Prob. 28WECh. 8.3 - Prob. 29WECh. 8.3 - Prob. 30WECh. 8.3 - Prob. 31WECh. 8.3 - Prob. 32WECh. 8.3 - Prob. 33WECh. 8.3 - Prob. 34WECh. 8.3 - Prob. 1MRECh. 8.3 - Prob. 2MRECh. 8.3 - Prob. 3MRECh. 8.3 - Prob. 4MRECh. 8.3 - Prob. 5MRECh. 8.3 - Prob. 6MRECh. 8.3 - Prob. 7MRECh. 8.3 - Prob. 8MRECh. 8.4 - Prob. 1OECh. 8.4 - Prob. 2OECh. 8.4 - Prob. 3OECh. 8.4 - Prob. 4OECh. 8.4 - Prob. 5OECh. 8.4 - Prob. 6OECh. 8.4 - Prob. 1WECh. 8.4 - Prob. 2WECh. 8.4 - Prob. 3WECh. 8.4 - Prob. 4WECh. 8.4 - Prob. 5WECh. 8.4 - Prob. 6WECh. 8.4 - Prob. 7WECh. 8.4 - Prob. 8WECh. 8.4 - Prob. 9WECh. 8.4 - Prob. 10WECh. 8.4 - Prob. 11WECh. 8.4 - Prob. 12WECh. 8.4 - Prob. 13WECh. 8.4 - Prob. 14WECh. 8.4 - Prob. 15WECh. 8.4 - Prob. 16WECh. 8.4 - Prob. 17WECh. 8.4 - Prob. 18WECh. 8.4 - Prob. 19WECh. 8.4 - Prob. 20WECh. 8.4 - Prob. 21WECh. 8.4 - Prob. 22WECh. 8.4 - Prob. 23WECh. 8.4 - Prob. 24WECh. 8.4 - Prob. 1ECh. 8.4 - Prob. 2ECh. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.5 - Prob. 1OECh. 8.5 - Prob. 2OECh. 8.5 - Prob. 3OECh. 8.5 - Prob. 4OECh. 8.5 - Prob. 5OECh. 8.5 - Prob. 6OECh. 8.5 - Prob. 1WECh. 8.5 - Prob. 2WECh. 8.5 - Prob. 3WECh. 8.5 - Prob. 4WECh. 8.5 - Prob. 5WECh. 8.5 - Prob. 6WECh. 8.5 - Prob. 7WECh. 8.5 - Prob. 8WECh. 8.5 - Prob. 9WECh. 8.5 - Prob. 10WECh. 8.5 - Prob. 11WECh. 8.5 - Prob. 12WECh. 8.5 - Prob. 13WECh. 8.5 - Prob. 14WECh. 8.5 - Prob. 15WECh. 8.5 - Prob. 16WECh. 8.5 - Prob. 17WECh. 8.5 - Prob. 18WECh. 8.5 - Prob. 19WECh. 8.5 - Prob. 20WECh. 8.5 - Prob. 21WECh. 8.5 - Prob. 22WECh. 8.5 - Prob. 23WECh. 8.5 - Prob. 24WECh. 8.5 - Prob. 25WECh. 8.5 - Prob. 26WECh. 8.5 - Prob. 27WECh. 8.5 - Prob. 28WECh. 8.5 - Prob. 29WECh. 8.5 - Prob. 30WECh. 8.5 - Prob. 31WECh. 8.5 - Prob. 32WECh. 8.5 - Prob. 33WECh. 8.5 - Prob. 34WECh. 8.5 - Prob. 35WECh. 8.5 - Prob. 36WECh. 8.5 - Prob. 37WECh. 8.5 - Prob. 38WECh. 8.5 - Prob. 39WECh. 8.5 - Prob. 1MRECh. 8.5 - Prob. 2MRECh. 8.5 - Prob. 3MRECh. 8.5 - Prob. 4MRECh. 8.5 - Prob. 5MRECh. 8.5 - Prob. 6MRECh. 8.5 - Prob. 7MRECh. 8.5 - Prob. 8MRECh. 8.5 - Prob. 9MRECh. 8.6 - Prob. 1OECh. 8.6 - Prob. 2OECh. 8.6 - Prob. 3OECh. 8.6 - Prob. 4OECh. 8.6 - Prob. 5OECh. 8.6 - Prob. 6OECh. 8.6 - Prob. 7OECh. 8.6 - Prob. 8OECh. 8.6 - Prob. 9OECh. 8.6 - Prob. 10OECh. 8.6 - Prob. 11OECh. 8.6 - Prob. 12OECh. 8.6 - Prob. 13OECh. 8.6 - Prob. 14OECh. 8.6 - Prob. 15OECh. 8.6 - Prob. 1WECh. 8.6 - Prob. 2WECh. 8.6 - Prob. 3WECh. 8.6 - Prob. 4WECh. 8.6 - Prob. 5WECh. 8.6 - Prob. 6WECh. 8.6 - Prob. 7WECh. 8.6 - Prob. 8WECh. 8.6 - Prob. 9WECh. 8.6 - Prob. 10WECh. 8.6 - Prob. 11WECh. 8.6 - Prob. 12WECh. 8.6 - Prob. 13WECh. 8.6 - Prob. 14WECh. 8.6 - Prob. 15WECh. 8.6 - Prob. 16WECh. 8.6 - Prob. 17WECh. 8.6 - Prob. 18WECh. 8.6 - Prob. 19WECh. 8.6 - Prob. 20WECh. 8.6 - Prob. 21WECh. 8.6 - Prob. 22WECh. 8.6 - Prob. 23WECh. 8.6 - Prob. 24WECh. 8.6 - Prob. 25WECh. 8.6 - Prob. 26WECh. 8.6 - Prob. 27WECh. 8.6 - Prob. 28WECh. 8.6 - Prob. 29WECh. 8.6 - Prob. 1STCh. 8.6 - Prob. 2STCh. 8.6 - Prob. 3STCh. 8.6 - Prob. 4STCh. 8.6 - Prob. 5STCh. 8.6 - Prob. 6STCh. 8.6 - Prob. 7STCh. 8.7 - Prob. 1OECh. 8.7 - Prob. 2OECh. 8.7 - Prob. 3OECh. 8.7 - Prob. 4OECh. 8.7 - Prob. 5OECh. 8.7 - Prob. 6OECh. 8.7 - Prob. 7OECh. 8.7 - Prob. 8OECh. 8.7 - Prob. 9OECh. 8.7 - Prob. 10OECh. 8.7 - Prob. 11OECh. 8.7 - Prob. 12OECh. 8.7 - Prob. 13OECh. 8.7 - Prob. 14OECh. 8.7 - Prob. 15OECh. 8.7 - Prob. 16OECh. 8.7 - Prob. 1WECh. 8.7 - Prob. 2WECh. 8.7 - Prob. 3WECh. 8.7 - Prob. 4WECh. 8.7 - Prob. 5WECh. 8.7 - Prob. 6WECh. 8.7 - Prob. 7WECh. 8.7 - Prob. 8WECh. 8.7 - Prob. 9WECh. 8.7 - Prob. 10WECh. 8.7 - Prob. 11WECh. 8.7 - Prob. 12WECh. 8.7 - Prob. 13WECh. 8.7 - Prob. 14WECh. 8.7 - Prob. 15WECh. 8.7 - Prob. 16WECh. 8.7 - Prob. 17WECh. 8.7 - Prob. 18WECh. 8.7 - Prob. 19WECh. 8.7 - Prob. 20WECh. 8.7 - Prob. 21WECh. 8.7 - Prob. 22WECh. 8.7 - Prob. 23WECh. 8.7 - Prob. 24WECh. 8.7 - Prob. 25WECh. 8.7 - Prob. 26WECh. 8.7 - Prob. 27WECh. 8.7 - Prob. 28WECh. 8.7 - Prob. 1MRECh. 8.7 - Prob. 2MRECh. 8.7 - Prob. 3MRECh. 8.7 - Prob. 4MRECh. 8.7 - Prob. 5MRECh. 8.7 - Prob. 6MRECh. 8.7 - Prob. 7MRECh. 8.7 - Prob. 8MRECh. 8.7 - Prob. 9MRECh. 8.7 - Prob. 10MRECh. 8.8 - Prob. 1OECh. 8.8 - Prob. 2OECh. 8.8 - Prob. 3OECh. 8.8 - Prob. 4OECh. 8.8 - Prob. 5OECh. 8.8 - Prob. 6OECh. 8.8 - Prob. 7OECh. 8.8 - Prob. 8OECh. 8.8 - Prob. 1WECh. 8.8 - Prob. 2WECh. 8.8 - Prob. 3WECh. 8.8 - Prob. 4WECh. 8.8 - Prob. 5WECh. 8.8 - Prob. 6WECh. 8.8 - Prob. 7WECh. 8.8 - Prob. 8WECh. 8.8 - Prob. 9WECh. 8.8 - Prob. 10WECh. 8.8 - Prob. 11WECh. 8.8 - Prob. 12WECh. 8.8 - Prob. 13WECh. 8.8 - Prob. 14WECh. 8.8 - Prob. 15WECh. 8.8 - Prob. 16WECh. 8.8 - Prob. 17WECh. 8.8 - Prob. 18WECh. 8.8 - Prob. 19WECh. 8.8 - Prob. 20WECh. 8.8 - Prob. 21WECh. 8.8 - Prob. 22WECh. 8.8 - Prob. 23WECh. 8.8 - Prob. 24WECh. 8.8 - Prob. 25WECh. 8.8 - Prob. 26WECh. 8.8 - Prob. 27WECh. 8.8 - Prob. 28WECh. 8.8 - Prob. 29WECh. 8.8 - Prob. 30WECh. 8.8 - Prob. 1ECh. 8.8 - Prob. 2ECh. 8.8 - Prob. 3ECh. 8.8 - Prob. 4ECh. 8.9 - Prob. 1OECh. 8.9 - Prob. 2OECh. 8.9 - Prob. 3OECh. 8.9 - Prob. 1WECh. 8.9 - Prob. 2WECh. 8.9 - Prob. 3WECh. 8.9 - Prob. 4WECh. 8.9 - Prob. 5WECh. 8.9 - Prob. 6WECh. 8.9 - Prob. 7WECh. 8.9 - Prob. 8WECh. 8.9 - Prob. 9WECh. 8.9 - Prob. 10WECh. 8.9 - Prob. 11WECh. 8.9 - Prob. 12WECh. 8.9 - Prob. 13WECh. 8.9 - Prob. 14WECh. 8.9 - Prob. 15WECh. 8.9 - Prob. 16WECh. 8.9 - Prob. 17WECh. 8.9 - Prob. 18WECh. 8.9 - Prob. 19WECh. 8.9 - Prob. 20WECh. 8.9 - Prob. 21WECh. 8.9 - Prob. 22WECh. 8.9 - Prob. 23WECh. 8.9 - Prob. 24WECh. 8.9 - Prob. 25WECh. 8.9 - Prob. 26WECh. 8.9 - Prob. 27WECh. 8.9 - Prob. 28WECh. 8.9 - Prob. 29WECh. 8.9 - Prob. 30WECh. 8.9 - Prob. 1CECh. 8.9 - Prob. 2CECh. 8.9 - Prob. 3CECh. 8.9 - Prob. 4CECh. 8.9 - Prob. 5CECh. 8.9 - Prob. 1STCh. 8.9 - Prob. 2STCh. 8.9 - Prob. 3STCh. 8.9 - Prob. 4STCh. 8.9 - Prob. 5STCh. 8 - Prob. 1CRCh. 8 - Prob. 2CRCh. 8 - Prob. 3CRCh. 8 - Prob. 4CRCh. 8 - Prob. 5CRCh. 8 - Prob. 6CRCh. 8 - Prob. 7CRCh. 8 - Prob. 8CRCh. 8 - Prob. 9CRCh. 8 - Prob. 10CRCh. 8 - Prob. 11CRCh. 8 - Prob. 12CRCh. 8 - Prob. 13CRCh. 8 - Prob. 1CTCh. 8 - Prob. 2CTCh. 8 - Prob. 3CTCh. 8 - Prob. 4CTCh. 8 - Prob. 5CTCh. 8 - Prob. 6CTCh. 8 - Prob. 7CTCh. 8 - Prob. 8CTCh. 8 - Prob. 9CT
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