Exercise 3.

Find a real root of the cubic equation in Exercise 2.

(This is for practice purposes only; to make the computations a little less messy, the root will turn out to be an integer, so one could use the Rational Zero test instead.)

Answer.

We want to find a real root of

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We set y=s-t, where

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The first equation yields

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Substituting this into (2) yields

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which can be rewritten as

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The quadratic formula tells us that

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We discard one of the solution to obtain

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Consequently

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so our solution is

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Substituting back for x, we see that

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What a complicated way of writing x=3!

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Helmut Knaust
Wed Jun 25 13:25:29 MDT 1997

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