BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

15th Edition

ISBN: 9781608408405

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Cengage Learning

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Question

Chapter 3.1, Problem 25E

(a)

To determine

The equation that has two real solution.

(a)

Expert Solution

Answer to Problem 25E

The required equation is x2=d for 0<d< ∞ .

Explanation of Solution

Given information:

The given form of the equation is x2=d .

Consider the given form of the equation x2=d .

For two real solution, the range of d is from 0<d< ∞ .

For example, consider an equation x2=4 .

x2=4x=±2

Thus, it has two real solution −2 and 2 .

Hence, the required equation is x2=d for 0<d< ∞ .

(b)

To determine

The equation that has one real solution.

(b)

Expert Solution

Answer to Problem 25E

The required equation is x2=0 .

Explanation of Solution

Given information:

The given form of the equation is x2=d .

Consider the given form of the equation x2=d .

For only one solution, the value of d is 0.

Substitute the value 0 for d in the equation x2=d .

x2=0x=0

Thus, it has only one real solution.

Hence, the required equation is x2=0 .

(c)

To determine

To calculate: The equation that has no real solution.

(c)

Expert Solution

Answer to Problem 25E

The required equation is x2=d for −∞>d>0 .

Explanation of Solution

Given information:

The given form of the equation is x2=d .

Calculation:

Consider the given form of the equation x2=d .

For two real solution, the range of d is from −∞>d>0 .

For example, consider an equation x2=−4 .

x2=−4x=−4x=±i2

Thus, it has two real solution −2 and 2 .

Hence, the required equation is x2=d for −∞>d>0 .

Chapter 3.1, Problem 24E

Chapter 3.1, Problem 26E

Chapter 3 Solutions

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E 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

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - 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