GeoGebra
You can solve equations either symbolically or numerically. GeoGebra solves them automatically when you enter them in CAS and click Symbolic Evaluation or Numeric Evaluation. Symbolic Evaluation gives you the exact solution, while Numeric Evaluation gives you the solution as a possibly approximated decimal number.
If you get as the output, then the equation has no solution. If you get , the equation has one solution, and if you get , the equation has two solutions. Note! Here and represent numbers.
GeoGebra Instruction 1
Solution in CAS
- 1.
- Open
CASunder
Viewin
Menu. - 2.
- Enter the equation in the
CASwindow. If the right-hand side of the equation is 0, you only need to type the expression on the left-hand side. - 3.
- Click
Solve
in the Menubarto get the exact solution, or clickSolve Numerically
in the Menubarto solve numerically.
Solving an equation graphically is the same as drawing the graph of the expressions on each side of the equation, and finding the -coordinate of the intersection between the graphs.
GeoGebra Instruction 2
Solution in Graphics View
- 1.
- Choose
Algebra ViewandGraphics Viewin the Viewmenu. - 2.
- Enter the expressions into two separate rows in the
Algebra Viewand pressEnter. Give the expressions fitting names. - 3.
- Find the intersection between the graphs. You do this by typing
Intersect(<object>, <object>)
where the objects correspond to the two expressions. Press
Enter. - 4.
- If the equation has any solutions, you can find them in the
Algebra View.
Example 1
Solve the equation
graphically, where
The picture below shows the solutions to the equation that you get by following the instructions above.
