1. Section 1.6 Other Types of Equations

2. Polynomial Equations

4. Example Solve by Factoring:

5. Example Solve by Factoring:

6. Graphing Equations You can find the solutions on the graphing calculator for the previous problem by moving all terms to one side, and graphing the equation. The zeros of the function are the solutions to the problem. X 4 -13X 2 +36=0

7. Radical Equations

8. A radical equation is an equation in which the variable occurs in a square root, cube root, or any higher root. We solve the equation by squaring both sides.

9. This new equation has two solutions, -4 and 4. By contrast, only 4 is a solution of the original equation, x=4. For this reason, when raising both sides of an equation to an even power, check proposed solutions in the original equation. Extra solutions may be introduced when you raise both sides of a radical equation to an even power. Such solutions, which are not solutions of the given equation are called extraneous solutions or extraneous roots.

12. Example Solve and check your answers:

13. Press Y= to type in the equation. For the negative use the white key in the bottom right hand side. For the use X use X,T,,,,n Graphing Calculator Move all terms to one side. See the next slide Press 2 nd Window in order to Set up the Table. Press the Graph key. Look for the zero of the function – the x intercept.

14. The Graphing Calculator’s Table Not a solution Is a solution Press 2 nd Graph in order to get the Table.

15. Solving an Equation That Has Two Radicals 1.Isolate a radical on one side. 2.Square both sides. 3.Repeat Step 1: Isolate the remaining radical on one side. 4.Repeat Step2: Square both sides. 5.Solve the resulting equation 6.Check the proposed solutions in the original equations.

16. Example Solve:

17. Equations with Rational Exponents

19. Example Solve:

20. Equations That Are Quadratic in Form

21. Some equations that are not quadratic can be written as quadratic equations using an appropriate substitution. Here are some examples: An equation that is quadratic in form is one that can be expressed as a quadratic equation using an appropriate substitution.

22. Example Simplify:

23. Example Simplify:

24. Equations Involving Absolute Value

26. Example Solve:

27. Absolute Value Graphs The graph may intersect the x axis at one point, no points or two points. Thus the equations could have one, or two solutions or no solutions.

28. (a) (b) (c) (d) Solve, and check your solutions:

29. (a) (b) (c) (d) Solve: