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Unit 4 Summary Sheet.Oct.20.09.period 1

Unit 4 Summary Sheet.Oct.20.09.period 1 - Unit 4 Summary...

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Unit 4 Summary Sheet 4.1 Solving Polynomial Equations: The solution to a polynomial equation f(x) = 0 are the zeros of the corresponding polynomial function, y = f(x) Polynomial equations can be solved using a variety of strategies: - Algebraically using factoring strategy - Graphing using a table of values, transformations, or a graphing calculator Side note: A polynomial function of degree “n” has n roots which may be of the form - Real roots (not all are distinct or different) - Complex roots (which occur in pairs) - Combination of the above Example: Solve the following: 4x³ - 12x² - x + 3 = 0 4x²(x-3) – 1(x-3) = 0 (The first and last two terms have common factor, so factor by grouping) (x -3) (4x² - 1) = 0 (x- 3) (2x – 1) (2x + 1) = 0 (set each of the factors equal to zero to solve) Therefore : x = 3, x = ½, x = -½ 4.2 Solving Linear Inequalities: You can solve a linear inequality using inverse operations in the same way you solve linear equations.
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