5.6 Find Rational Zeros
The Rational Zero Theorem
If f(x) = anxn + ... + a1x + a0 has integer
coefficients, then every rational zero of f
has the following form:
p = factor of constant term a0
q factor of leading coefficient an
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Examples: List the possible rational zeros
of the function using the Rational zero
Theorem.
1.) f(x) = x3 - 3x + 28
2.) f(x) = 2x4 + 6x3 - 7x + 9
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Examples: Find all real zeros. One zero is
given.
1.) f(x) = x3 - 12x2 + 35x - 24 ; x = 1
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Examples: Find all real zeros of
the function.
1.) f(x) = 2x3 + 2x2 - 8x - 8
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2.) h(x) = 2x4 + 9x3 + 5x2 + 3x - 4
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3.) f(x) = x5 - 3x4 - 5x3 + 15x2 + 4x - 12
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