a .
To identify: the points on the line at which the polynomial
a .
Answer to Problem 86E
Explanation of Solution
Calculation:
The polynomial
That is, when
So, the points on the number line on which polynomial is zero are
b.
To write: the sign of each factor and the sign of the product
b.
Answer to Problem 86E
For interval
For interval
For interval
Explanation of Solution
Consider the given line:
It divides the number line into three subintervals namely
Clearly
For interval
And as product of two negative numbers is always positive, so the product
For interval
And as product of a negative number and a positive number is always negative, so the product
For interval
And as product of two positive numbers is always positive, so the product
c.
To identify: the x-values where the polynomial changes signs
c.
Answer to Problem 86E
Explanation of Solution
Calculation:
The values where a polynomial can change sign are its zeros.
The zeros of polynomial
Now from part (b),
For interval
For interval
For interval
Thus, the polynomial changes sign at both the points a and b.
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