Linear Sentences in One Variable
Polynomial Functions
The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x-axis; that is, the real zero of a function is the x-intercept(s) of the graph of the function.
Example 1: Find the zeros of the function f ( x)= x2 − 8 x − 9.
Find
x so that
f (
x)=
x2 − 8
x − 9=0.
f (
x) can be factored, so begin there.
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Therefore, the zeros of the function
f (
x)=
x2 − 8
x − 9 are −1 and 9. This means
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If a polynomial function with integer coefficients has real zeros, then they are either rational or irrational values. Rational zeros can be found by using the rational zero theorem.
