Understanding Extraneous Solutions in Radical Equations

The video tutorial explains how to determine the value of D that makes x = -3 an extraneous solution for a given radical equation. It begins by defining extraneous solutions and how they occur, particularly when squaring both sides of an equation. The tutorial then guides through solving the equation, rearranging it into a quadratic form, and finding the value of D. Finally, it verifies the solution, showing that x = -3 is indeed extraneous for the original equation when D equals 2.

What is an extraneous solution?

• A solution that is derived from incorrect assumptions.

• A solution that is always correct.

• A solution that is a byproduct of the solving process but does not satisfy the original equation.

• A solution that satisfies the original equation.

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CCSS.HSA.REI.A.2

How do extraneous solutions typically arise?

• By dividing both sides of an equation by a variable.

• By adding a constant to both sides of an equation.

• By multiplying both sides of an equation by zero.

• By squaring both sides of an equation.

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CCSS.HSA.REI.A.2

What happens when you square both sides of an equation?

• The equation becomes unsolvable.

• The equation becomes linear.

• You may introduce extraneous solutions.

• The equation remains unchanged.

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CCSS.8.EE.A.2

What is the result of squaring a negative number?

• Zero.

• A negative number.

• An undefined value.

• A positive number.

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CCSS.HSA.REI.A.2

Why is x = -3 an extraneous solution for the yellow equation?

• Because it is a solution to both equations.

• Because it is not a solution to any equation.

• Because it satisfies the purple equation but not the yellow equation.

• Because it satisfies the original equation.

Tags

CCSS.HSA.REI.A.2

What value of D makes x = -3 an extraneous solution?

• D = 3

• D = 2

• D = 1

• D = 0

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CCSS.8.EE.A.2

What is the principal root of 16?

• 2

• 4

• 8

• -4

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CCSS.6.EE.B.7

What is the result of adding 6 to both sides of the equation -4 = D - 6?

• D = 4

• D = -2

• D = 2

• D = 0

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CCSS.HSA.REI.A.2

Why does x = -3 not satisfy the original equation when D = 2?

• Because it results in the same value on each side.

• Because it results in different values on each side.

• Because it results in a positive value on both sides.

• Because it results in a negative value on both sides.

Tags

CCSS.HSA.REI.A.2

What is the significance of verifying the solution in the context of extraneous solutions?

• To prove the solution is always extraneous.

• To ensure the solution satisfies the original equation.

• To demonstrate the solution is irrelevant.

• To confirm the solution is incorrect.

Tags

CCSS.HSA.REI.A.2