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Find the complex zeros of the polynomial? first correct answer gets 10 points?
f(x)= x^3 - 5x^2 +9x -5
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- quinticLv 61 decade agoFavorite Answer
By inspection, f(1) = 0, so by the factor theorem x - 1 is a factor of f.
Factorizing: f(x) = (x - 1)(x² - 4x + 5).
So the other two zeros are given by x² - 4x + 5 = 0.
Completing the square, (x - 2)² + 1 = 0.
Thus (x - 2)² = -1, and x - 2 = ±i.
So the other two zeros are x = 2 ± i.
Source(s): http://en.wikipedia.org/wiki/Factor_theorem
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