For Exercises 85–90, determine if the statement is true or false. If a statement is false, explain why. 85. A polynomial with real coefficients of degree 4 must have at least one real zero. 86. Given f(x) = 2ix – (3 + 6i)x' + 5x + 7, if a + bi is a zero of f(x), then a – bi must also be a zero. 87. The graph of a 10th-degree polynomial must cross the x-axis exactly once. 88. Suppose that f(x) is a polynomial, and that a and b are real numbers where a < b. If f(a) < 0 and f(b) < 0, then f(x) has no real zeros on the interval [a, b]. 89. If c is a zero of a polynomial f(x), with degree n > 2 90. If b is an upper bound for the real zeros of a polynomial, fx) then all other zeros of f(x) are zeros of then -b is a lower bound for the real zeros of the polynomial. 91. Given that x - c divides evenly into a polynomial f(x), 92. a. Use the quadratic formula to solve x - 7x + 5 = 0. b. Write x – 7x + 5 as a product of linear factors. which statements are true? a. x - c is a factor of f(x). b. c is a zero of f(x). c. The remainder of f(x) ÷ (x – c) is 0. d. c is a solution (root) of the equation f(x) = 0. 93. a. Use the intermediate value theorem to show that f(x) = 2 - 7x + 4 has a real zero on the interval [2, 3]. 94. Show that x - a is a factor of x" – d" for any positive integer n and constant a. b. Find the zeros.
For Exercises 85–90, determine if the statement is true or false. If a statement is false, explain why. 85. A polynomial with real coefficients of degree 4 must have at least one real zero. 86. Given f(x) = 2ix – (3 + 6i)x' + 5x + 7, if a + bi is a zero of f(x), then a – bi must also be a zero. 87. The graph of a 10th-degree polynomial must cross the x-axis exactly once. 88. Suppose that f(x) is a polynomial, and that a and b are real numbers where a < b. If f(a) < 0 and f(b) < 0, then f(x) has no real zeros on the interval [a, b]. 89. If c is a zero of a polynomial f(x), with degree n > 2 90. If b is an upper bound for the real zeros of a polynomial, fx) then all other zeros of f(x) are zeros of then -b is a lower bound for the real zeros of the polynomial. 91. Given that x - c divides evenly into a polynomial f(x), 92. a. Use the quadratic formula to solve x - 7x + 5 = 0. b. Write x – 7x + 5 as a product of linear factors. which statements are true? a. x - c is a factor of f(x). b. c is a zero of f(x). c. The remainder of f(x) ÷ (x – c) is 0. d. c is a solution (root) of the equation f(x) = 0. 93. a. Use the intermediate value theorem to show that f(x) = 2 - 7x + 4 has a real zero on the interval [2, 3]. 94. Show that x - a is a factor of x" – d" for any positive integer n and constant a. b. Find the zeros.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![For Exercises 85–90, determine if the statement is true or false. If a statement is false, explain why.
85. A polynomial with real coefficients of degree 4 must
have at least one real zero.
86. Given f(x) = 2ix – (3 + 6i)x' + 5x + 7, if a + bi is
a zero of f(x), then a – bi must also be a zero.
87. The graph of a 10th-degree polynomial must cross the
x-axis exactly once.
88. Suppose that f(x) is a polynomial, and that a and b are
real numbers where a < b. If f(a) < 0 and f(b) < 0,
then f(x) has no real zeros on the interval [a, b].
89. If c is a zero of a polynomial f(x), with degree n > 2
90. If b is an upper bound for the real zeros of a polynomial,
fx)
then all other zeros of f(x) are zeros of
then -b is a lower bound for the real zeros of the
polynomial.
91. Given that x - c divides evenly into a polynomial f(x),
92. a. Use the quadratic formula to solve
x - 7x + 5 = 0.
b. Write x – 7x + 5 as a product of linear factors.
which statements are true?
a. x - c is a factor of f(x).
b. c is a zero of f(x).
c. The remainder of f(x) ÷ (x – c) is 0.
d. c is a solution (root) of the equation f(x) = 0.
93. a. Use the intermediate value theorem to show that f(x) =
2 - 7x + 4 has a real zero on the interval [2, 3].
94. Show that x - a is a factor of x" – d" for any positive
integer n and constant a.
b. Find the zeros.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a440353-127d-4e33-bbe5-77d900a60397%2F1388c779-84a3-4879-9c88-0ffb102d7865%2Fd703mxl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For Exercises 85–90, determine if the statement is true or false. If a statement is false, explain why.
85. A polynomial with real coefficients of degree 4 must
have at least one real zero.
86. Given f(x) = 2ix – (3 + 6i)x' + 5x + 7, if a + bi is
a zero of f(x), then a – bi must also be a zero.
87. The graph of a 10th-degree polynomial must cross the
x-axis exactly once.
88. Suppose that f(x) is a polynomial, and that a and b are
real numbers where a < b. If f(a) < 0 and f(b) < 0,
then f(x) has no real zeros on the interval [a, b].
89. If c is a zero of a polynomial f(x), with degree n > 2
90. If b is an upper bound for the real zeros of a polynomial,
fx)
then all other zeros of f(x) are zeros of
then -b is a lower bound for the real zeros of the
polynomial.
91. Given that x - c divides evenly into a polynomial f(x),
92. a. Use the quadratic formula to solve
x - 7x + 5 = 0.
b. Write x – 7x + 5 as a product of linear factors.
which statements are true?
a. x - c is a factor of f(x).
b. c is a zero of f(x).
c. The remainder of f(x) ÷ (x – c) is 0.
d. c is a solution (root) of the equation f(x) = 0.
93. a. Use the intermediate value theorem to show that f(x) =
2 - 7x + 4 has a real zero on the interval [2, 3].
94. Show that x - a is a factor of x" – d" for any positive
integer n and constant a.
b. Find the zeros.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning