Descartes Rule of Signs Positive real zeros = Negative real zeros =

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Presentation transcript:

Descartes Rule of Signs Positive real zeros = Negative real zeros = 2.5 cont. Provides more specific information about the number of real zeros a polynomial can have. The number of sign changes of f(x) or less than this by an even integer. The number of sign changes of f(-x) or less than this by an even integer. Descartes Rule of Signs Positive real zeros = Negative real zeros = 1

Example Determine the possible number of positive and negative real zeros of f(x) = x3 + 7x2 + x + 7 You try one Determine the possible number of positive and negative real zeros of f(x) = x3 + 2x2 + 5x + 4 2

Linear Factorization Theorem Enables us to find a polynomial function when the zeros are known. An nth-degree polynomial can be expressed as the product of a nonzero constant and n linear factors, where each linear factor has a leading coefficient of 1. 3

Example Find an nth-degree polynomial function with real coefficients satisfying the given conditions. n = 3; 4 and 2i are zeros; f(-1) = 50 4

You try one Find an nth-degree polynomial function with real coefficients satisfying the given conditions. n = 3; -3 and i are zeros; f(1) = 8 5

P. 336 #17 – 37 odd 6