How do I find multiplicities for functions?

Expert Answers
embizze eNotes educator| Certified Educator

I assume that you are asking for the multiplicities of the roots. For example `f(x)=x^3+x^2-5x+3` factors as `f(x)=(x-1)^2(x+3)` , so f(x) has roots 1 and -3, with 1 as a double root or a root of multiplicity 2.

Generally you factor the polynomial -- the power on the linear factor is the multiplicity. From the graph you know if the multiplicity is even or odd -- with an even multiplicity the graph touches the x-axis without going "through" it. In other words, the function has a local maximum or minimum at that zero. If the multiplicity is odd, the graph goes through the axis.

For the example above:

pramodpandey | Student

Let f(x)=ax^2+bx+c

We wish to find


`` So we can find multiplicity of f as







`` This method we apply