   Chapter 0.5, Problem 38E

Chapter
Section
Textbook Problem

Find all possible real solutions of each equation in Exercises 31–44. y 3 − 2 y 2 − 2 y − 3 = 0

To determine

To calculate: The all real solutions in the polynomial equation y32y22y3=0.

Explanation

Given Information:

The provided polynomial equation is y32y22y3=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 y32y22y3=0.

First determine the single solution in this cubic equation y32y22y3=0

Compare the equation y32y22y3=0 with the standard cubic equation ax3+bx2+cx+d=0.

a=1 and d=3

Therefore, possible factor of 1 is x=±1 and 3 is x=±1, x=±2 and x=±3.

First try y=3 substitute in the provided polynomial equation y32y22y3=0, (3)32(3)22(3)3=?0            271863=?0                               0=0

Which is true

Therefore, y3 is a factor of the polynomial y32y22y3=0.

In order to find other two values of x, divide y32y22y3=0 by y3, y3y2+y+1y32y22y3         y33y2_               y22y  &#

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