Find the polynomial f(x) that has the roots of -2, 3 of multiplicity 2. Explain how you would verify the zeros of f(x).

Question

anonymous · Answer

Multiplicity refers to what it is raised to the power of.

Roots/Solutions/Zeroes of -2 and 3 are (x+2)(x-3)

Can you figure it out from this info?

anonymous · Answer

i dont think so

anonymous · Answer

Roots = Solutions = Zeroes

Thought you should know that these terms all apply to the same concept.

anonymous · Answer

Alright, so let's continue then.

anonymous · Answer

so those are already the solutions?

anonymous · Answer

Those are the factors. Ok so we need to know which factor the multiplicity of 2 is referring too. For example. The factor -2 is described by the (x+2) term. (It becomes zero when we plug in -2). If it's multiplicity is 2, that means it looks like (x-2)^2.

Now if we are talking about the term 3, of which (x-3) describes the factor, where if we plug in 3 for x we get 0, right, if it is of multiplicity 2 then it looks like (x-3)^2.... 


is this making any sense?

anonymous · Answer

oh i see

anonymous · Answer

Find the polynomial f(x) that has the roots of -2, 3 of multiplicity 2. Explain how you would verify the zeros of f(x).

$$f(x) = (x-3)^{2}(x+2)$$

OR

$$f(x) = (x-3)(x+2)^{2}$$

Depending on which term you are applying the multiplicity of 2 to.