### Solve

You can easily solve equations using the TI-89 graphing calculator.  The key decision for the user is whether to work in the real or the complex number system.  For example, let’s solve the quadratic equation, 2x2 - 5x +12 = 0.

To solve the equation in the real number system, press F2 to select the algebra menu, press 1 to select 1:solve( , enter the equation, then press , (comma)  X  )  ENTER.  The TI-89 responds with the answer false, indicating that this equation has no real roots.

To obtain the complex roots, follow the above procedure with the following exception.  Instead of selecting 1:solve( , select A:Complex , then select 1:cSolve.  The complex roots are

In particular, note that the option 1:solve yields solutions only in the real number system; whereas, cSolve yields solutions in the complex number system.

You may also solve an equation with a constraint.  This is handy, for example, in solving trigonometric equations.  For example, let’s solve sin(2q ) = 1 for 0 £ q < 2p.  The appropriate syntax is:

solve(equation,variable) | constraint.

Here, the entry line is

solve(sin(2x)=1,x) | 0 £ x and x < 2p

Consult the test menu for details on how to enter inequalities and the “and”.