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

campbell_st · Answer

so it means that the the function is 

f(x) = (x + 2)(x -3)^2 

if a root is x = -2 then the factor is (x + 2)
                x = 3   then the factor is (x - 3)

multiplicity of 2 means the factor is squared. 

so the general form is 

$$f(x) = a(x +2)(x -3)^2$$

to test it, select a point on the curve..... substitute x and y and then you'll find the left is a multiple of the right.... then multiple is the value of a

anonymous · Answer

Thanks you!!! :D

directrix · Answer

Does the prepositional phrase "of multiplicity 2" describe the root 3 only or does the phrase describe BOTH roots 3 and -2?

directrix · Answer

If both, then we would have this--> f(x) = (x + 2)^2 (x -3)^2

anonymous · Answer

Okay thanks!!! :D)

directrix · Answer

Enjoyed working on the Descartes problem.