1.4 Radical Equations, Equations Quadratic In Form, Factorable Equations
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1.4 Radical Equations, Equations Quadratic In Form, Factorable Equations

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1.4 Radical Equations, Equations Quadratic In Form, Factorable Equations 1.4 Radical Equations, Equations Quadratic In Form, Factorable Equations Presentation Transcript

  • College Algebra 1.4 I. Radical Equations; II. Equations Quadratic in Form; III. Factorable Equations
  • I. Solving Radical Equations
    • 1. Isolate a radical.
    • 2. Raise each SIDE to the appropriate power
    • ( square a square root, cube a cube root, etc .) and simplify.
    • 3. (Repeat until no radicals remain.)
    • 4. Solve the resulting equation.
    • 5. CHECK for EXTRANEOUS SOLUTIONS.
    • Note: Extraneous solutions are solutions which do not solve the original equation. They are Extra(neous).
  • extraneous solution (does not work in the original equation)
  • II. “Quadratic Form” Equations – The degree of one term is twice the degree of the other term.
    • Method 1: Substitution
    • 1. Substitute another variable, say u, for the original variable to obtain the form:
    • au 2 + bu + c = 0
    • 2. Solve this quadratic equation (for u) using
    • any method you wish.
    • 3. Substitute the solutions for u to find the
    • solutions for the original variable.
  •  
  • III. Higher Degree Polynomial Equations
    • ● Try to solve by Factoring.
    • ● Remember to first look for a ___________
    • ● Remember the different methods of Factoring for different situations: trinomials, difference of squares, sum/difference of cubes, grouping, etc.
    • ● Remember that the solutions to f(x)= 0 are: ________________________________
  • Solve the equation: