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

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