Concept explainers
To find : all the zeros of the function
Answer to Problem 73E
The zeros of the function are:
Explanation of Solution
Given information:
Concept Involved:
Complex Zeros Occur in Conjugate Pairs: Let f be a polynomial function that has real coefficients. If
Synthetic Division (for a Cubic Polynomial):To divide
In case when we have a polynomial with a missing term, insert placeholders with zero coefficients for missing powers of the variable. Vertical pattern: Add terms in columns Diagonal pattern: Multiply results by k. This algorithm for synthetic division works only for divisors of the form x - k. Remember that |
The Division Algorithm: If
Graph:
Interpretation:
From the graph of the function we can pick possible zeros of the function as
Calculation:
Use synthetic division to find the other zeros of the function
If
To find other zeros of the polynomial
We can solve this equation using completing the square method by subtracting 74 on both sides of the equation
Simplify on both sides of the equation
In order to make the left side expression as perfect square trinomial, we need to add square of half of coefficient of x on both sides
Simplify on right side of the equation
Write the left side as a perfect square
Split the right side of the equation as product of two numbers
Take square root on both sides
Simplifying square root on both sides of the equation
Replace
Subtracting 7 on both sides of the equation
Simplify in left side of the equation
List the zeros of the functions given:
Conclusion:
The zeros of the given function
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning