Solving Polynomials.

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Presentation transcript:

Solving Polynomials

Warm Up Find the zeros of the following polynomials. 1. f(x) = x(x – 1)(x + 5) 2. g(x) = x3(x – 1)2(x + 5)7 Find the polynomial function with the given zeros. 1. 0, 1, -5

Multiplicity The multiplicity of a zero is the power of the factor that it came from. Find the zeros and their multiplicities for the following. 1. f(x) = (3x + 2)4(x – 7) 2. g(x) = (x + 3)4(5 – 4x)5(2x + 1) 3. h(x) = (9x – 2)2(x – 4)3(x + 6)5

Try This Find the polynomial (in factored form) with the following zeros and multiplicities. -1 (multiplicity 2), 0 (multiplicity 3), 4 3 (multiplicity 3), -5 0, -7 (multiplicity 2), 6 (multiplicity 4)

Fundamental Theorem of Algebra If f(x) is a polynomial of degree n where n > 0, then the equation f(x) = 0 has exactly n solutions provided each solution with multiplicity 2 is counted twice, each solution with multiplicity 3 is counted as 3 solutions and so on.

Try This For each of the following state how many solutions the polynomial has. f(x) = x4 + 3x2 – x + 7 g(x) = -3x2 – 4x5 + 5x4 – 3x + 1 h(x) = (x + 1) 2(x – 3)(x + 6) 3 f(x) = (2x – 1)(3x + 2)(x – 4) 7

Solving Polynomials Solve x3 – x2 – 30x = 0 If given no other information you will have to start by factoring or looking at the graph.

Solving Polynomials Solve x4 + x3 – 12x2 = 0 if (x + 4) is a factor Solve x3 – 8x2 + 22x – 20 = 0 if 2 is a root.