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Unformatted text preview: topic of this section. Well, that’s kind of the topic of this
section. In general, finding all the zeroes of any polynomial is a fairly difficult process. In this
section we will give a process that will find all rational (i.e. integer or fractional) zeroes of a
polynomial. We will be able to use the process for finding all the zeroes of a polynomial
provided all but at most two of the zeroes are rational. If more than two of the zeroes are not
rational then this process will not find all of the zeroes.
We will need the following theorem to get us started on this process.
Rational Root Theorem
If the rational number x = b
is a zero of the nth degree polynomial,
P ( x ) = sx n + L + t where all the coefficients are integers then b will be a factor of t and c will be a factor of s.
Note that in order for this theorem to work then the zero must be reduced to lowest terms. In
other words it will work for 4
but not necessarily for
15 Let’s verify the results of this theorem with an example. Example 1 Ve...
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- Spring '12