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Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248

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Chapter
Section
BuyFindarrow_forward

Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248
Textbook Problem

Find all possible real solutions of each equation in Exercises 31–44.

x 3 1 = 0

To determine

To calculate: The all real solutions in the polynomial equation x31=0.

Explanation

Given Information:

The provided polynomial equation is x31=0.

Formula used:

Zero product rule:

An equation ab=0 is true if and only if a=0 or b=0, both

A product is zero if and only if at least one factor is zero

The value of x in the equation ax2+bx+c=0 can be given by the quadratic formula,

x=b±b24ac2a where a,b and c are real numbers with a0.

Calculation:

Consider the polynomial equation x31=0.

First determine the single solution in this cubic equation x31=0

Compare the equation x31=0 with the standard cubic equation ax3+bx2+cx+d=0.

a=1 and d=1

Therefore, possible factor of 1 is x=±1 and 1 is x=±1

First try x=1 substitute in the provided polynomial equation x31=0, (1)31=?0    11=?00=0

This is true

Therefore, x1 is a factor of the polynomial x31=0.

In order to find other two values of x, divide x31=0 by x1, x1x2+x+1x3+0x2+0x1x3x2_       x2+0x       x2x_            �

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