Extraneous Solutions of Radical Equations

What is an extraneous solution ?

• A solution of an equation that does not satisfy the original equation.

  
  

• A solution to an equation that satisfies the original equation.

• When both solutions fit the original equation

• When there is no solution to the equation

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CCSS.HSA.REI.A.2

Which of the following is a characteristic of an extraneous solution?

• It is always a negative number.

• It appears as a result of certain algebraic manipulations.

• It is the only solution to nonlinear equations.

• It can be found without solving the equation.

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CCSS.HSA.REI.A.2

How can you identify an extraneous solution?

• By graphing the equation and finding the x-intercepts.

• By substituting the solution back into the original equation.

• By checking if the solution is a prime number.

• By solving the equation using only arithmetic operations.

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CCSS.HSA.REI.A.2

Why do extraneous solutions occur?

• Due to errors in calculation.

• Because the equation has no real solutions.

• When the equation is only solvable in complex numbers.

• During the process of solving the equation, like squaring both sides.

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CCSS.HSA.REI.A.2

• 3

• -3

• 2

• 0

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CCSS.HSA.REI.A.2

• 9

• -9

• 7

• -7

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CCSS.HSA.REI.A.2

• 3

• 2

• -3

• -2

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CCSS.HSA.REI.A.2

• 6

• 9

• -6

• -9

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CCSS.HSA.REI.A.2

• 1

• -1

• 2

• -2

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CCSS.HSA.REI.A.2

• 7

• 5

• -7

• -5

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CCSS.HSA.REI.A.2