HP -15C Owner's Handbook Manual page 183

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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.
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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.
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10 "
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Section 13: Finding the Roots of an Equation
Display
5.0000
Display
5.0000
0.0000
Display
0.0000
–10
–2.0000
–2.0000
0.0000
The desired root.
A previous estimate of the
root.
Value of the function at the
root showing that f(x) = 0.
Initial estimates.
The second root.
A previous estimate of the
root.
Value of f(x) at second root.
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