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“Is it better to be feared or respected? And I say, is it too much to ask for both?” 3.7: Complex Zeros Fundamental Theorem of Algebra 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. f (x) x 4 3x 3 19x 2 27x 252 f ( x) x3 13x 2 36 f ( x) x6 x5 2 x 4 3x3 40 x 2 137 x 58 Complex Zeros Find the complex zeros of the polynomial function, and write as a product of linear factors. f (x) x 4 13x 2 36 Complex Zeros Find the complex zeros of the polynomial function, and write as a product of linear factors. f (x) x 4 3x 3 19x 2 27x 252 Complex Zeros Find the complex zeros of the polynomial function, and write as a product of linear factors. f ( x) 3x 4 2 x3 33x 2 82 x 40 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 r a bi 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. Complex Zeros Use the given zero to find the remaining zeros of the given function. f (x) 2x 4 x 3 7x 2 4 x 4; zero : 2i Complex Zeros Use the given zero to find the remaining zeros of the given function. f (x) x 4 9x 2 14 x 30; zero : 1 3i “Don’t worry Wilson, I’ll do all the paddling. You just hang on!” 3.7 Complex Zeros Homework: Page 237 #7 – 31 Odd