SOLUTION: Find the zeros for the following polynomial function and give the multiplicity for each zero. For each zero, state whether the graph crosses the x-axis or touches the x-axis and tu

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the zeros for the following polynomial function and give the multiplicity for each zero. For each zero, state whether the graph crosses the x-axis or touches the x-axis and tu      Log On


   

Question 935052: Find the zeros for the following polynomial function and give the multiplicity for each zero. For each zero, state whether the graph crosses the x-axis or touches the x-axis and turns around.
+f%28x%29=5%28x-4%29%28x%2B6%29%5E3+
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Zero of 4, multiplicity 1.
Zero of -6, multiplicity 3.

The zeros are the critical values. Touch or cross? Check the three intervals around the critical values.

Less than -6:
(-)(-)=(+), positive.

Between -6 and 4:
(-), and x=0 is a convenient test value.
negative.

Greater than 4:
Positive.

The graph of f(x) CROSSES the horizontal axis at the zeros of f.