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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. ________________________________________ 3. 2i , 1 , 5, and − 2 2 ________________________________________ 3, and 4 4. ________________________________________ 2, − 5, and − 3i ________________________________________ 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 ________________________________________ ________________________________________ 7. x 4 + 4 x 3 + 4 x 2 + 64 x − 192 = 0 8. x 3 + 3 x 2 + 9 x + 27 = 0 ________________________________________ ________________________________________ 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). _________________________________________________________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 142 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 ______________________ 2. P (x ) = 2 x 5 − 5 x + 10 3. P (x ) = 3 x 4 + 2 x ___________________ __________________ 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 ________________________________________ ________________________________________ 7. 2i a. How many zeros does this function have? _______________________________ b. Write the conjugate pair for the complex root. _______________________________ c. Write the factored expression. _______________________________ d. Multiply the binomials. _______________________________ 8. −2 and 3 9. 3 and 2 + i ________________________________________ ________________________________________ Solve the equation by finding all roots. 10. x 3 − 6 x 2 − 2 x + 12 = 0 _________________________________________________________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 144