Question

guide me though this please?(:





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).

Answer 1

I am really not sure because I am not good with these! @cebroski

Answer 2

THANK YOU!!

Answer 3

f(0)=0-1?

Answer 4

ohhh. okay.. then what?

Answer 5

x=1

Answer 6

I have limited time, I need to get to the answer quick! can you explain it quickly all at once? Ill try to read over it afterwards and make myself understand it.

Answer 7

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 - (-2))*(x - (3))*(x - (3))
f(x) = (x + 2)*(x - 3)*(x - 3)
f(x) = x^3 - 4x^2 - 3x + 18

Verify by plugging in the zeros (or roots) in for x and making sure they give you an equation that has both sides equal to each other.

Verify that
f(-2) = 0
f(3) = 0

Answer 8

do you still need help?

Answer 9

After you've got an equation, a further test is to graph it and check the behavior at the roots. A root with an odd multiplicity (1, 3, 5, etc.) will cross the x-axis. A root with an even multiplicity touches the axis and retreats.

I see @cebroski has interpreted the question as having only the root 3 have a multiplicity 2. In that case, we'll have one axis crossing and one axis touch.