Polynomial Functions and Complex Zeros

Precal Unit 3

Complex Zeros Lesson

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Find all zeros of the polynomial functions below. Simplify all irrational and complex solutions.

3. f(x) = x⁴ - 16; ​ ​

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and ​

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4. f(x) = -2x³ - 16; ​

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and ​

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±2

±2i

-2

1 ± i√3

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Find all zeros of the polynomial function below. . Simplify all irrational and complex solutions.

5. f(x) = x³ - 2x² + x - 2: ​

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and ​

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6. f(x) = 3x³ - 4x² + 36x - 48; ​

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and ​​

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Find all the zeros of the function below. Write in simplest form.

7. f(x) = 2x⁵ -5x⁴ -2x + 5

• $$x\ =\ \left\{\pm i\right\}$$  

• $$x\ =\ \left\{\frac{2}{5}\right\}$$  

• $$x\ =\ \left\{\pm1\right\}$$  

• $$x\ =\ \left\{\frac{5}{2}\right\}$$  

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Find all the real zeros of the following function. Simplify answers.

8. f(x) = x⁴ + 7x³ - x - 7

• $$x=\left\{\pm1\right\}$$  

• $$x=\left\{-7\right\}$$  

• $$x=\left\{1\right\}$$  

• $$x\ =\left\{\frac{-1\pm i\sqrt[]{3}}{2}\right\}$$  

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