Rational Root Theorem.notebook
November 01, 2011
The Rational Root Theorem
The Rational Zero Theorem gives a list of possible
rational zeros of a polynomial function.
The theorem gives all possible rational roots of a
polynomial equation. Not every number in the list will
be a zero of the function, but every rational zero of the
The Rational Root Theorem
If f (x) = anxn + an-1xn-1 +&+ a1x + a0 has integer
coefficients and (where
is reduced) is a
rational zero, then p is a factor of the constant
term a0 and q is a factor of the leading coefficient an.
polynomial function will appear somewhere in the list.
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EXAMPLE: Using
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the Rational Zero Theorem
List all possible rational zeros of f (x) = 15x3 + 14x2 - 3x – 2.
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