Section 13: Finding the Roots of an Equation 183

Keystrokes

Display

 

´_0

5.0000

The desired root.

After the routine finds and displays the root, you can ensure that the displayed number is indeed a root of f(x) = 0 by checking the stack. You have seen that the display (X-register) contains the desired root. The Y-register contains a previous estimate of the root, which should be very close to the displayed root. The Z-register contains the value of your function evaluated at the displayed root.

Keystrokes

Display

 

)

5.0000

A previous estimate of the

 

 

root.

)

0.0000

Value of the function at the

 

 

root showing that f(x) = 0.

Quadratic equations, such as the one you are solving, can have two roots. If you specify two new initial estimates, you can check for a second root. Try estimates of 0 and -10 to look for a negative root.

Keystrokes

Display

0 v

0.0000

10 “

–10

´_0

–2.0000

)

–2.0000

)

0.0000

Initial estimates.

The second root.

A previous estimate of the root.

Value of f(x) at second root.