Concept explainers
To calculate : the real roots of the given equation
Answer to Problem 18WE
The roots of the equation are
Explanation of Solution
Given information :
The polynomial equation:
Formula used :
Intermediate-Value Theorem:
If P is a polynomial function with real coefficients, and m is any number between P (a) and P ( b ), then there is at least one number c between a and b for which P ( c ) = m .
Calculation :
As per the given problem,
Consider the given equation:
By Descartes’s rule
The table of values at the left below shows that
The table of values at the right above, shows that the negative root is between
The table of values at the left below, shows that one of the positive roots is between
The table of values at the right below, shows that the other positive root is between
The roots of P are
Chapter 8 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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