The Fundamental Theorem of Algebra

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Presentation transcript:

The Fundamental Theorem of Algebra (simplified)

Warm-Up Challenge The number is less than 1000. The sum of the digits is 16. The sum of the first digit and the last digit is 11. The second digit is 3 more than the first. What’s my number? Answer: 259

1. The Fundamental Theorem oF Algebra A polynomial of degree n has exactly n roots when counting multiple roots and non-real solutions. How many roots? f(x) = 5x7 – 4x3 + 3x – 9 7 f(x) = -5x3 + 2x4 – x + 13 4

2. Solve a) x3 – 8x2 + 25x – 26 = 0 Answer: x = 2, x = 3 + 2i, x = 3 – 2i b) x4 – 4x3 – 2x2 + 20x – 15 = 0 Answer: x = 1, x = 3, x = √5, x = -√5

3. Write an equation with the given roots Answer: f(x) = x3 + 3x2 – 10x b) ± 3 , ± 6i Answer: f(x) = x4 + 33x2 – 108

4. If this is a 6th degree polynomial, describe the roots.