# Thread: Polynomial of nth degree that includes zeroes

1. ## Polynomial of nth degree that includes zeroes

Find a polynomial f(x) of degree 6 such that 0,3 are zeroes of multiplicity 3 and f(2) = -24. Write the polynomial in decreasing order of exponents.

How do I do the above? What does it mean by zeroes of multiplicity 3???

2. Originally Posted by mwok
Find a polynomial f(x) of degree 6 such that 0,3 are zeroes of multiplicity 3 and f(2) = -24. Write the polynomial in decreasing order of exponents.

How do I do the above? What does it mean by zeroes of multiplicity 3???
Multiplicity means the power it is raised to. So we have that

$f(x)=Ax^3(x-3)^3$

Now to find A we use our conditino

$-24=A(2)^3(-1)^3\Rightarrow{A=3}$

So your function is $f(x)=3x^3(x-3)^3$