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• In Exercise 1 you showed that the polynomial r³ – 4x + 2 has a zero in R. This result can be generalized to any polynomial of odd degree: Let P(r) be a polynomial of odd degree P(x) = x²n+1 + a2nx?n + ….+ ao (we may assume that a2n+1 = 1). - What is lim, P(x)? Hint: Factor out z²n+1 and use the fact lim, = 0. - What is lim,→-∞ P(x)? Hint: Factor out 2n+1. - Use the IVP to show that any polynomial of odd degree must have a zero in R

• In Exercise 1 you showed that the polynomial r³ – 4x + 2 has a zero in R. This result can be generalized to any polynomial of odd degree: Let P(r) be a polynomial of odd degree P(x) = x²n+1 + a2nx?n + ….+ ao (we may assume that a2n+1 = 1). - What is lim, P(x)? Hint: Factor out z²n+1 and use the fact lim, = 0. - What is lim,→-∞ P(x)? Hint: Factor out 2n+1. - Use the IVP to show that any polynomial of odd degree must have a zero in R

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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• In Exercise 1 you showed that the polynomial r³ – 4x + 2 has a zero in R. This result can be generalized to any polynomial of odd degree: Let P(r) be a polynomial of odd degree P(x) = x²n+1 + a2nx?n + ….+ ao (we may assume that a2n+1 = 1). - What is lim, P(x)? Hint: Factor out z²n+1 and use the fact lim, = 0. - What is lim,→-∞ P(x)? Hint: Factor out 2n+1. - Use the IVP to show that any polynomial of odd degree must have a zero in R
Transcribed Image Text:• In Exercise 1 you showed that the polynomial r³ – 4x + 2 has a zero in R. This result can be generalized to any polynomial of odd degree: Let P(r) be a polynomial of odd degree P(x) = x²n+1 + a2nx?n + ….+ ao (we may assume that a2n+1 = 1). - What is lim, P(x)? Hint: Factor out z²n+1 and use the fact lim, = 0. - What is lim,→-∞ P(x)? Hint: Factor out 2n+1. - Use the IVP to show that any polynomial of odd degree must have a zero in R
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