Concept explainers
The solution of the equation
Answer to Problem 68AYU
Solution:
The real solution of the equation
Explanation of Solution
Given Information:
The equation
Step-1: The degree of the polynomial function
Step-2: Since there are 2 variations in the sign of the non-zero coefficients of
There are 2 variations in the sign of the non-zero coefficients of
Step-3: By the Rational Zero Theorem, all possible rational zeroes are of the form
In the polynomial function
Factors of the constant term
Factors of the leading term
Therefore, all the possible rational zeros are:
Simplifies and reduces to
Thus, all the potential rational zeros of the polynomial function
Now, test
Here, since the remainder is 0,
To write the factors of
Here,
Any solution to this depressed equation is also a zero of
Repeat step-3 to find zeros of this depressed equation.
In the polynomial
Factors of the constant term
Factors of the leading term
Therefore, all possible rational zeros are:
Simplifies and reduces to
Thus, all the potential rational zeros of the depressed equation
Now, test
Here, since the remainder is
Now, test
Here, since the remainder is 0,
Use the entries in the bottom row of the synthetic division to continue the factoring of
Here,
Thus, the real solution of the equation
Chapter 4 Solutions
Precalculus
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