AnswersCommon Core Algebra II 2014 - MA3111 CRRadical Equations and Extraneous Roots

Radical Equations and Extraneous Roots Answers

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1
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Use the equation How many potential solutions are there?

Answer not available
2
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How many extraneous solutions are there?

Answer not available
3

The solution to the equation is x =

Answer not available
4

Which of the following occurs within the solution process for ?

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A
squaring both sides once
B
squaring both sides twice
C
cubing both sides once
D
cubing both sides twice
5

The potential solution of is x =

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Answer:

-3

6

Which statement about is true?

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A
–3 is an extraneous solution because solutions can never be negative.
B
–3 is an extraneous solution because substituting it into the original equation gives a false statement.
C
–3 is a valid solution because substituting it into the original equation gives a true statement.
7

Which of the following is a valid step in the solution of

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A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
8

Which statement aboutis true?

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A
x = 1 is an extraneous solution.
B
x = 1 is a true solution
C
x = 3 is an extraneous solution.
D
x = 3 is a true solution.
11

Which of the following best describes how to solve ?

Question illustration
A
Square both sides once, then solve the resulting linear equation.
B
Square both sides twice, then solve the resulting linear equation.
C
Square both sides once, then solve the resulting quadratic equation.
D
Square both sides twice, then solve the resulting quadratic equation.
12

A potential solution of is .

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Answer:

1/2

13

Which statement about is true?

Question illustration
A
is an extraneous solution.
Option A
B
is a true solution.
Option B
C
x = 2 is an extraneous solution.
D
x = 2 is a true solution.
15

Which statement about is true?

Answer not available
17

After eliminating radicals, what quadratic equation can you solve to find the potential solutions of ?

Question illustration
A
x² - 2x - 3 = 0
B
x² + 2x + 5 = 0
C
x² - 4x - 3 = 0
D
2x² - 4x - 4 = 0
18

Check all of the following that are a solution of .

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A
–3
B
–1
C
1
D
3
21

What is the solution to the equation ?x =

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Answer:

5

23

What is the solution to the equation ?x =

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Answer:

23

25

Luca solved an equation as shown, and verified that his solution was correct.Explain what Luca’s error is and why his answer is not completely correct.

Answer:

Luca incorrectly squares the right side: (√(x − 3) + 1)² includes the cross term 2√(x − 3), which he omitted. This causes him to miss the other solution, x = 7. Both x = 3 and x = 7 satisfy the original equation, so his answer is not complete.

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