Find the zeros for the following polynomial function and give the multiplicity for each zero state whether the graph crosses the x-axis or touches and turns around... f(x)=9(x+8)(x+6)^3
What is the value of the zero with the smaller multiplicity?

Question

Find the zeros for the following polynomial function and give the multiplicity for each zero state whether the graph crosses the x-axis or touches and turns around... f(x)=9(x+8)(x+6)^3
What is the value of the zero with the smaller multiplicity?

jdoe0001 · Answer

well, if you set the equation to 0
that is $\bf  0=9(x+8)(x+6)^3$
the roots are really obvious
$\bf0= 9(x+8)(x+6)^3 \implies 0 =9(x+8)(x+6)(x+6)(x+6)$

jdoe0001 · Answer

now you have really 2 non-repeated roots
the one raised to 3, is really the root with the multiplicity of 3
so the multiplicity will be the exponent of the binomial for that root
so the other will have the "smaller" multiplicity

jdoe0001 · Answer

does it cross or just touch the x-axis?
well, keep in mind that, if the multiplicity, the exponent, is EVEN, it "touches" only, if it's ODD, it "crosses"