Download Finding Complex Solutions of Polynomial Equations

Name ________________________________________ Date __________________ Class __________________
LESSON
7-2
Finding Complex Solutions of Polynomial Equations
Practice and Problem Solving: A/B
Write the simplest polynomial function with the given roots.
1. 1, 4, and −3
2.
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3. 2i ,
1
, 5, and − 2
2
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3, and 4
4.
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2, − 5, and − 3i
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Solve each equation by finding all roots.
5. x 4 − 2 x 3 − 14 x 2 − 2 x − 15 = 0
6. x 4 − 16 = 0
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7. x 4 + 4 x 3 + 4 x 2 + 64 x − 192 = 0
8. x 3 + 3 x 2 + 9 x + 27 = 0
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Solve.
9. An electrical circuit is designed such that its output voltage, V, measured in
volts, can be either positive or negative. The voltage of the circuit passes
through zero at t = 1, 2, and 7 seconds. Write the simplest polynomial
describing the voltage V(t).
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Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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Name ________________________________________ Date __________________ Class __________________
LESSON
7-2
Finding Complex Solutions of Polynomial Equations
Practice and Problem Solving: Modified
Identify the number of zeros for each function. The first one is done
for you.
1. P (x ) = x 3 + 2 x 2 − 12 x + 1
3
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2. P (x ) = 2 x 5 − 5 x + 10
3. P (x ) = 3 x 4 + 2 x
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Write the simplest polynomial function with the given zeros. The first
one is done for you.
4. −1, 0, and 2
a. Write the factored expression.
P (x ) = x (x + 1)(x − 2)
b. Multiply the first two factors.
P (x ) = (x 2 + x )(x − 2)
c. Multiply the result by the remaining factor.
d. Combine like terms.
5. −3, 1, and 5
6. −4, −1, and 1
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7. 2i
a. How many zeros does this function have?
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b. Write the conjugate pair for the complex root.
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c. Write the factored expression.
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d. Multiply the binomials.
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8. −2 and 3
9. 3 and 2 + i
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Solve the equation by finding all roots.
10. x 3 − 6 x 2 − 2 x + 12 = 0
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Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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