Warm-up Find the solutions to the polynomial equation.

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Presentation transcript:

Warm-up Find the solutions to the polynomial equation.

Classwork: #1, 6, 10,11, 13, 14, 19, 20, 21, 26, 27, 30

Section 6-5: Theorems about Roots of Polynomial Equations Goal 1.02: Define and compute with complex numbers. Goal 1.03: Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems.

Find a polynomial equation with the given roots ex1: – 4, 4i - 4i must also be a zero (x + 4)(x – 4i)(x + 4i) (x + 4)(x 2 + 4i – 4i – 16i 2 ) (x + 4)(x ) x x + 4x x 3 + 4x x + 64 ex2: - 1, 3 + i, 3 – i must also be a zero (x + 1)[x – (3 + i)][x – (3 – i)] (x + 1)(x – 3 – i)(x – 3 + i) (x + 1)(x 2 – 3x + xi – 3x + 9 – 3i – xi + 3i – i 2 ) (x + 1)(x 2 – 6x + 10) x 3 – 6x x + x 2 – 6x + 10 x 3 – 5x 2 + 2x + 10

ex3: 6, 3 – 2i 3 + 2i must also be a zero (x – 6 )[x – (3 – 2i)][x – (3 + 2i)] (x – 6 )(x – 3 + 2i)(x – 3 – 2i) (x – 6 )(x 2 – 3x – 2xi – 3x i + 2xi – 6i – 4i 2 ) (x – 6 )(x 2 – 6x + 13) x 3 – 6x x – 6x x – 78 x 3 – 12x x – 78 ex4: 1,  6 -  6 must also be a zero (x – 1)(x -  6)(x +  6) (x – 1)(x 2 +  6x -  6x -  36) (x – 1)(x 2 – 6) x 3 – 6x – x x 3 – x 2 – 6x + 6

Extra Example

Classwork/ Homework Study for 15 minutes each day this weekend.