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

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Presentation transcript:

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

Solve the equation.

 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.

 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.

 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.

 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.

 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

 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)

 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. ?

 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. ? ?

 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. ?

 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. ?

 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.

 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.

 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.

 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.

 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.

 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.

 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)