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Answer the following justifying your answers with examples or by stating theorem(s) used: a) Is it possible to have a cubic polynomial with real coefficients and only two real zeros? b) Does N(x) = 3x* – 5x3 + 3x2 + 1 have any negative real zeros?

Answer the following justifying your answers with examples or by stating theorem(s) used: a) Is it possible to have a cubic polynomial with real coefficients and only two real zeros? b) Does N(x) = 3x* – 5x3 + 3x2 + 1 have any negative real zeros?

Calculus: Early Transcendentals
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...
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**Question 3:** Answer the following justifying your answers with examples or by stating theorem(s) used: a) Is it possible to have a cubic polynomial with real coefficients and only two real zeros? b) Does \( N(x) = 3x^4 - 5x^3 + 3x^2 + 1 \) have any negative real zeros? **Explanation:** The questions require applying knowledge of polynomial functions and their properties. - Part a) explores the nature of polynomial roots and the Fundamental Theorem of Algebra, which states that a polynomial of degree \( n \) has exactly \( n \) roots (real or complex) considering multiplicity. - Part b) involves analyzing the given polynomial to determine if there are any negative real solutions, possibly using techniques such as Descartes' Rule of Signs or other analytical methods.
Transcribed Image Text:**Question 3:** Answer the following justifying your answers with examples or by stating theorem(s) used: a) Is it possible to have a cubic polynomial with real coefficients and only two real zeros? b) Does \( N(x) = 3x^4 - 5x^3 + 3x^2 + 1 \) have any negative real zeros? **Explanation:** The questions require applying knowledge of polynomial functions and their properties. - Part a) explores the nature of polynomial roots and the Fundamental Theorem of Algebra, which states that a polynomial of degree \( n \) has exactly \( n \) roots (real or complex) considering multiplicity. - Part b) involves analyzing the given polynomial to determine if there are any negative real solutions, possibly using techniques such as Descartes' Rule of Signs or other analytical methods.
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