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“Is it better to be feared or respected? And I say, is it too much to ask for both?”

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Presentation on theme: "“Is it better to be feared or respected? And I say, is it too much to ask for both?”"— Presentation transcript:

1 “Is it better to be feared or respected? And I say, is it too much to ask for both?”

2 3.7: Complex Zeros

3 If f (x) is a polynomial of degree n > 0, the f has exactly n linear factors and therefore n zeros in the complex plane a+bi. Fundamental Theorem of Algebra

4 Complex Zeros Find the complex zeros of the polynomial function, and write as a product of linear factors.

5 Complex Zeros Find the complex zeros of the polynomial function, and write as a product of linear factors.

6 Complex Zeros Find the complex zeros of the polynomial function, and write as a product of linear factors.

7 Conjugate Pairs Theorem Let f (x) be a complex polynomial whose coefficients are real numbers. If r = a + bi is a zero of f, then the complex conjugate is also a zero of f. Find a polynomial f of degree 4 in standard form whose coefficients are real numbers and has zeros 1, 2, and 2 + i.

8 Complex Zeros Use the given zero to find the remaining zeros of the given function.

9 Complex Zeros Use the given zero to find the remaining zeros of the given function.

10 “Don’t worry Wilson, I’ll do all the paddling. You just hang on!”

11 3.7 Complex Zeros Homework: Page 237 #7 – 31 Odd


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