Solve Quadratic Equations Using the Square Root Property Quiz
The question sheet
Reveal any answer as you study-
According to the Square Root Property, if x² = k and k ≥ 0, then:
- x = k only
- x = 2k
- x = √k or x = −√k
- x = k²
Reveal answer
Answer: x = √k or x = −√k
Source evidence
PDF page 1164: If x = k , and k ≥ 0 , then x = k or x = − k .
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The Square Root Property gives how many solutions to an equation of the form x² = k?
- Two
- One
- Three
- Four
Reveal answer
Answer: Two
Source evidence
PDF page 1164: 2 Notice that the Square Root Property gives two solutions to an equation of the form x = k : the principal square root of
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What is the solution to x² = 169 in Example 10.1?
- x = ±12
- x = ±169
- x = ±13
- x = 169
Reveal answer
Answer: x = ±13
Source evidence
PDF page 1165: EXAMPLE 10.1 2 Solve: x = 169 . Solution 2 x = 169 Use the Square Root Property.
PDF page 1165: Rewrite to show two solutions.
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Why can't x² = 7 be solved by factoring?
- 7 is not a perfect square
- 7 is odd
- 7 is negative
- 7 is a perfect square
Reveal answer
Answer: 7 is not a perfect square
Source evidence
PDF page 1164: 2 2 We can easily use factoring to find the solutions of similar equations, like x = 16 and x = 25 , because 16 and 25 are 2 perfect squares. But what happens when we have an equation like x = 7 ? Since 7 is not a perfect square, we cannot solve the equation by factoring. 2 These equations are all of the form x = k . We defined the square root of a number in this way: 2
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To use the Square Root Property, the coefficient of the variable term must equal:
- 0
- k
- 2
- 1
Reveal answer
Answer: 1
Source evidence
PDF page 1166: To use the Square Root Property, the coefficient of the variable term must equal 1. In the next example, we must divide both sides of the equation by 5 before using the Square Root Property.
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In Example 10.3, to solve 5m² = 80, what must be done first?
- Factor the left side
- Multiply both sides by 5
- Divide both sides by 5
- Subtract 80
Reveal answer
Answer: Divide both sides by 5
Source evidence
PDF page 1166: EXAMPLE 10.3 2 Solve: 5m = 80 . Solution
PDF page 1166: 5m 80 = Divide by 5 to make its cofficient 1. 5 5
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When k < 0 in x² = k, what happens?
- Two solutions
- There is no real solution
- k becomes positive
- One solution
Reveal answer
Answer: There is no real solution
Source evidence
PDF page 1166: 2 The Square Root Property started by stating, ‘If x = k , and k ≥ 0 ’. What will happen if k < 0 ? This will be the case in the next example.
PDF page 1167: The −24 is not a real number. There is no real solution.
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In Example 10.7, solving (x − 3)² = 16 leads to which two equations?
- x − 3 = 4, x − 3 = −4
- x = 3 ± 16
- x − 3 = 16
- x = 4, x = −4
Reveal answer
Answer: x − 3 = 4, x − 3 = −4
Source evidence
PDF page 1169: x − 3 = 4, x − 3 = −4
PDF page 1169: Write as two equations.
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What does the text say to do when solutions have fractions inside the radicals?
- Round to a whole number
- Leave them as is
- Rationalize the denominator
- Factor the numerator
Reveal answer
Answer: Rationalize the denominator
Source evidence
PDF page 1168: The solutions to some equations may have fractions inside the radicals. When this happens, we must rationalize the denominator.
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How can we take the square root of a fraction?
- Square root of numerator and denominator
- Only the numerator
- Take root of denominator only
- Multiply first
Reveal answer
Answer: Square root of numerator and denominator
Source evidence
PDF page 1169: Remember, when we take the square root of a fraction, we can take the square root of the numerator and denominator
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In Example 10.10, solving (x − 2)² + 3 = 30, what is done first?
- Use the Square Root Property
- Isolate the binomial term
- Check the solutions
- Simplify the radical
Reveal answer
Answer: Isolate the binomial term
Source evidence
PDF page 1170: We will start the solution to the next example by isolating the binomial. EXAMPLE 10.10 2 Solve: (x − 2) + 3 = 30 . Solution 2 (x − 2) + 3 = 30 2 Isolate the binomial term. (x − 2) = 27 Use the Square Root Property.
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A quadratic equation has the form ax² + bx + c = 0 with what condition?
- a ≠ 0
- c = 0
- a = 0
- b = 0
Reveal answer
Answer: a ≠ 0
Source evidence
PDF page 1164: 2 Quadratic equations are equations of the form ax + bx + c = 0 , where a ≠ 0 . They differ from linear equations by including a term with the variable raised to the second power. We use different methods to solve quadratic equations than linear equations, because just adding, subtracting, multiplying, and dividing terms will not isolate the variable. We have seen that some quadratic equations can be solved by factoring. In this chapter, we will use three other methods to solve quadratic equations. 2
Elementary Algebra 2e
Elementary Algebra 2e by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
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