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Display
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RCL 2
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Deflation for second root.
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–
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÷
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Find the fourth root.
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Keystrokes
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Display
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g P/R
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–
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1.0929
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– 07
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10 CHS ENTER
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Same initial estimates.
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20 CHS
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f SOLVE 2
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Fourth root.
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STO 3
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Stores root for reference.
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R R
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Deflated function value near zero.
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Using the same initial estimates each time, you have found
four roots for this equation involving a fourth-degree
polynomial. However, the last two roots are quite close to
each other and are actually one root (with a multiplicity of 2).
That is why the root was not eliminated when you tried
deflation once at this root. (Round-off error causes the
original function to have small positive and negative values
for values of x between 8.4999 and 8.5001; for
x = 8.5 the function is exactly zero.)
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In general, you will not know in advance the multiplicity of the root you are trying
to eliminate. If, after you have attempted to eliminate a root,
SOLVE finds that same root again, you can proceed in a
number of ways:
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Use different initial estimates with the deflated function in an attempt
to search for a different root.
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Use deflation again in an attempt to eliminate a multiple root. If you do
not know the multiplicity of the root, you may need to repeat this a number
of times.
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