4-3 Solving Quadratic Equations by Factoring Solve each equation by factoring.
49. SOLUTION: Write the equation with right side equal to zero.
Find factors of 12(–5) = –60 whose sum is –4. –10(6) = –60 and –10 + 6 = –4
Therefore, the roots are
51.
SOLUTION: Write the equation with right side equal to zero.
Divide each side of the equation by 4.
Find factors of 4(9) = 36 whose sum is 12.
6(6) = 36 and 6 + 6 = 12
Therefore, the only repeated root is eSolutions Manual - Powered by Cognero
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Therefore, the rootsEquations are 4-3 Solving Quadratic by Factoring
51.
SOLUTION: Write the equation with right side equal to zero.
Divide each side of the equation by 4.
Find factors of 4(9) = 36 whose sum is 12.
6(6) = 36 and 6 + 6 = 12
Therefore, the only repeated root is
53.
SOLUTION: Factor out the GCF of the left side, 4.
2
2
2
Use the identity a – b = (a + b)(a – b) to factor x – 36.
Use the Zero Product Property.
Therefore, the roots are 6 and –6.
eSolutions ManualTHEATER - Powered by Cognero MOVIE
55.
A company plans to build a large multiplex theater. The financial analyst told her managerPage 2 2 that the profit function for their theater was P(x) = –x + 48x – 512, where x is the number of movie screens, and P (x) is the profit earned in thousands of dollars. Determine the range of production of movie screens that will
4-3 Solving Quadratic by Factoring Therefore, the rootsEquations are 6 and –6.
55. MOVIE THEATER A company plans to build a large multiplex theater. The financial analyst told her manager 2 that the profit function for their theater was P(x) = –x + 48x – 512, where x is the number of movie screens, and P (x) is the profit earned in thousands of dollars. Determine the range of production of movie screens that will guarantee that the company will not lose money.
SOLUTION: For the company not to loose money, the profit should be non-negative. That is, at least zero.
Factor out –1.
2
Factor x – 48x + 512.
Find factors of 512 whose sum is –48 . –16(–32) = 512 and –16 + (–32) = –48
A total of 16 to 32 screens will guarantee that company will not lose money.
Write a quadratic equation in standard form with the given root(s).
57. 3.4, 0.6
SOLUTION: Write the pattern.
Replace p and q with 3.4 and 0.6.
Use the FOIL method to multiply. eSolutions Manual - Powered by Cognero
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A total of 16 to 32 screens will guarantee that company will not lose money. 4-3 Solving Quadratic Equations by Factoring
Write a quadratic equation in standard form with the given root(s).
57. 3.4, 0.6
SOLUTION: Write the pattern.
Replace p and q with 3.4 and 0.6.
Use the FOIL method to multiply.
Multiply each side by 25.
Solve each equation by factoring.
59.
SOLUTION: Write the equation with right side equal to zero.
Divide each side by 5.
Find factors of 2(–3) = –6 whose sum is 5.
–1(6) = –6 and –1 + 6 = 5
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4-3 Solving Quadratic Equations by Factoring Solve each equation by factoring.
59.
SOLUTION: Write the equation with right side equal to zero.
Divide each side by 5.
Find factors of 2(–3) = –6 whose sum is 5.
–1(6) = –6 and –1 + 6 = 5
Therefore, the roots are
61.
SOLUTION: Write the equation with right side equal to zero.
Multiply each side by 4.
Find factors of 4(–5) = –20 whose sum is 1.
5(–4) = –20 and 5 + (–4) = 1
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Therefore, the roots are
4-3 Solving Quadratic Equations by Factoring 61.
SOLUTION: Write the equation with right side equal to zero.
Multiply each side by 4.
Find factors of 4(–5) = –20 whose sum is 1.
5(–4) = –20 and 5 + (–4) = 1
Therefore, the roots are
63.
SOLUTION: Write the equation with right side equal to zero.
Multiply each side by 4.
Find factors of 12(–15) = –180 whose sum is 8.
18(–10) = 8 and 18 + (–10) = 8
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Therefore, the roots are 4-3 Solving Quadratic Equations by Factoring
63.
SOLUTION: Write the equation with right side equal to zero.
Multiply each side by 4.
Find factors of 12(–15) = –180 whose sum is 8.
18(–10) = 8 and 18 + (–10) = 8
Therefore, the roots are
Factor each polynomial.
71.
SOLUTION: Factor 3a from the first two terms and 8b from the last two terms.
Factor 6 – 8y from the two terms.
73.
eSolutions Manual - Powered by Cognero SOLUTION:
2
Factor 6b from all the three terms.
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4-3 Solving Quadratic Equations by Factoring 73.
SOLUTION: 2
Factor 6b from all the three terms.
75.
SOLUTION: Factor 4x from the first two terms and –6y from the last two terms.
Factor 8a + 3b from the two terms.
77.
SOLUTION: Rearrange the terms to group the terms with common factors.
Factor 5a from the first two terms and 2b from the last two terms.
2
2
Factor x – y from the two terms.
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4-3 Solving Quadratic Equations by Factoring
77.
SOLUTION: Rearrange the terms to group the terms with common factors.
Factor 5a from the first two terms and 2b from the last two terms.
2
2
Factor x – y from the two terms.
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