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Example 4 Solving a Quartic Equation Chapter 6.4 Solve the equation.  2009 PBLPathways.

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Presentation on theme: "Example 4 Solving a Quartic Equation Chapter 6.4 Solve the equation.  2009 PBLPathways."— Presentation transcript:

1 example 4 Solving a Quartic Equation Chapter 6.4 Solve the equation.  2009 PBLPathways

2 Solve the equation.

3  2009 PBLPathways Solve the equation. Solving Cubic and Quartic Equations of the Form f(x) = 0 1.Determine the possible rational solutions of f(x) = 0. 2.Graph y = f(x) to see if any of the values from Step 1 are x-intercepts. The x- intercepts are also solutions to f(x) = 0. 3.Find the factors associated with the x-intercepts from Step 2. 4.Use synthetic division to divide f (x) by the factors from Step 3 to confirm the graphical solutions and find additional factors. Continue until a quadratic factor remains. 5.Use factoring or the quadratic formula to find the solutions associated with the quadratic factor. These solutions are also solutions to f(x) = 0.

4  2009 PBLPathways Solve the equation. Solving Cubic and Quartic Equations of the Form f(x) = 0 1.Determine the possible rational solutions of f(x) = 0.

5  2009 PBLPathways Solve the equation. Solving Cubic and Quartic Equations of the Form f(x) = 0 1.Determine the possible rational solutions of f(x) = 0.

6  2009 PBLPathways Solve the equation. Solving Cubic and Quartic Equations of the Form f(x) = 0 1.Determine the possible rational solutions of f(x) = 0.

7  2009 PBLPathways Solve the equation. Solving Cubic and Quartic Equations of the Form f(x) = 0 2.Graph y = f(x) to see if any of the values from Step 1 are x-intercepts. The x- intercepts are also solutions to f(x) = 0. x y

8  2009 PBLPathways Solve the equation. Solving Cubic and Quartic Equations of the Form f(x) = 0 2.Graph y = f(x) to see if any of the values from Step 1 are x-intercepts. The x- intercepts are also solutions to f(x) = 0. x y (-2, 0) (-1, 0)

9  2009 PBLPathways Solve the equation. Solving Cubic and Quartic Equations of the Form f(x) = 0 3.Find the factors associated with the x-intercepts from Step 2. ?

10  2009 PBLPathways Solve the equation. Solving Cubic and Quartic Equations of the Form f(x) = 0 4.Use synthetic division to divide f (x) by the factors from Step 3 to confirm the graphical solutions and find additional factors. Continue until a quadratic factor remains. ? ?

11  2009 PBLPathways Solve the equation. Solving Cubic and Quartic Equations of the Form f(x) = 0 4.Use synthetic division to divide f (x) by the factors from Step 3 to confirm the graphical solutions and find additional factors. Continue until a quadratic factor remains. ?

12  2009 PBLPathways Solve the equation. Solving Cubic and Quartic Equations of the Form f(x) = 0 4.Use synthetic division to divide f (x) by the factors from Step 3 to confirm the graphical solutions and find additional factors. Continue until a quadratic factor remains. ?

13  2009 PBLPathways Solve the equation. Solving Cubic and Quartic Equations of the Form f(x) = 0 4.Use synthetic division to divide f (x) by the factors from Step 3 to confirm the graphical solutions and find additional factors. Continue until a quadratic factor remains.

14  2009 PBLPathways Solve the equation. Solving Cubic and Quartic Equations of the Form f(x) = 0 5.Use factoring or the quadratic formula to find the solutions associated with the quadratic factor. These solutions are also solutions to f(x) = 0.

15  2009 PBLPathways Solve the equation. Solving Cubic and Quartic Equations of the Form f(x) = 0 5.Use factoring or the quadratic formula to find the solutions associated with the quadratic factor. These solutions are also solutions to f(x) = 0.

16  2009 PBLPathways Solve the equation. Solving Cubic and Quartic Equations of the Form f(x) = 0 5.Use factoring or the quadratic formula to find the solutions associated with the quadratic factor. These solutions are also solutions to f(x) = 0.

17  2009 PBLPathways Solve the equation. Solving Cubic and Quartic Equations of the Form f(x) = 0 5.Use factoring or the quadratic formula to find the solutions associated with the quadratic factor. These solutions are also solutions to f(x) = 0.

18  2009 PBLPathways Solve the equation. Solving Cubic and Quartic Equations of the Form f(x) = 0 5.Use factoring or the quadratic formula to find the solutions associated with the quadratic factor. These solutions are also solutions to f(x) = 0.

19  2009 PBLPathways Solve the equation. Solving Cubic and Quartic Equations of the Form f(x) = 0 5.Use factoring or the quadratic formula to find the solutions associated with the quadratic factor. These solutions are also solutions to f(x) = 0. x y (-2, 0) (-1, 0) (0.58, 0) (-2.58, 0)

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