Precalculus: Mathematics for Calculus - 6th Edition

6th Edition

ISBN: 9780840068071

Author: Stewart, James, Redlin, Lothar, Watson, Saleem

Publisher: Cengage Learning

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Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

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Question

Chapter 3.6, Problem 15E

To determine

To find: the zeroes of polynomial P(x)=x6−1

Expert Solution

Answer to Problem 15E

The zeroes of polynomial P(x)=x6−1 is −1,1,−12−3i2,−12+3i2,12−3i2,12+3i2

Explanation of Solution

Given information: The polynomial is P(x)=x6−1

Calculation: For the zeroes of P(x) solve the equation P(x)=0 for x

P(x)=0⇒x6−1=0 ⇒(x3)2−12=0(x3−1)(x3+1)=0(x−1)(x2+x+1)(x+1)(x2−x+1)=0x−1=0x=1x+1=0x=−1x2+x+1=0x1,2=−b±b2−4ac2ax1,2=−1±12−4(1)(1)2(1)x1,2=−1±−32x=−12−3i2&x=−12+3i2x2−x+1=0x1,2=−b±b2−4ac2ax1,2=1±(−1)2−4(1)(1)2(1)x1,2=1±−32x=12−3i2&x=12+3i2

The zeroes of the polynomial function P(x) are −1,1,−12−3i2,−12+3i2,12−3i2,12+3i2

To determine

To calculate: the factored form of polynomial P(x)=x6−1

Expert Solution

Answer to Problem 15E

The factored form of polynomial P(x)=x6−1 is P(x)=(x−1),(x+1),(x+1+32i),(x+1−32i),(x−1−32i),(x−1+32i)

Explanation of Solution

Given information: The polynomial is P(x)=x6−1

Calculation: According to the factor theorem if c is a zero of a polynomial function P(x) the binomial (x−c) is a factor of this polynomial

The zeroes of the polynomial is expressed as

P(x)=(x−1),(x+1),(x+1+32i),(x+1−32i),(x−1−32i),(x−1+32i)

Hence,

The factored form of polynomial P(x) is

P(x)=(x−1)(x+1)(x+1+32i)(x+1−32i)(x−1−32i)(x−1+32i)

Chapter 3.6, Problem 14E

Chapter 3.6, Problem 16E

Chapter 3 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 3.1 - To put the quadratic function f(x)=ax2+bx+c in...Ch. 3.1 - The quadratic function f(x) = a(x - h)2 + k is in...Ch. 3.1 - The graph of f(x) = 3(x - 2)2 - 6 is a parabola...Ch. 3.1 - The graph of f(x) = -3(x - 2)2 - 6 is a parabola...Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

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the zeroes of polynomial P ( x ) = x 6 − 1

Concept explainers

Videos

To find: the zeroes of polynomial P(x)=x6−1

Answer to Problem 15E

Explanation of Solution

To calculate: the factored form of polynomial P(x)=x6−1

Answer to Problem 15E

Explanation of Solution

Chapter 3 Solutions