Question

how do I write a polynomial function when you are given the zeros of that function???

Answer 1

Write the polynomials having the following zeros:
1) -1, 1, 6
If the polynomial has these zeros, then you can write:
x = -1, so x+1 = 0
x = 1, so x-1 = 0
x = 6, so x-6 = 0

Answer 2

Well you know that when in factored form...a polynomial looks something like

(x - something)(x + something) etc...

Well if you are given the zeros...you merely see what would make that function = 0 given them

Example...if you know the zeros of a function are 3 and -5

(x - 3)(x + 5)

why does this work? because when you plug in x = 3 or x = 5 ...that equation = 0

Answer 3

so i would make those equal to 0?
confused...

Answer 4

Notice that allot of the work we do with polynomials is a direct result of what we call the zero product rule

if ab=0 then a= 0, b=0, or they both equal 0.

this is not the case for ab=1 (there are infinite solutions a=1,b=1 or a=1/2 b = 2......

so if we can get from the form of ax^2+bx+c (not there are three terms) into something like this (x-c)(x+d), this is only one term, then we can solve for (x-c)(x+d)=0

Answer 5

Supposing you have this equation:
(x+2)(x-3)=0
Could you solve that?

Answer 6

oh my lord.....
its x^2 -3x+2x-6 = 0???????????????

Answer 7

x+2=0 or x-3=0
x=-2 or x=3

Answer 8

Do you understand that?

Answer 9

It's a simple yes or no question.

Answer 10

nvm i got it

Answer 11

Could you do that backwards? What if I said x = -2 and x = 3. What factors produced those answers. Could you tell me?

Answer 12

x+2 =0 and x-3=0

Answer 13

Perfect!! So your problem gives you the answers and asks you to write the factors. What answers did it give you?

Answer 14

2 and -3...

Answer 15

So, what factors did those answers come from?

Answer 16

-2 and 3? im getin so confused

Answer 17

The factors would be x-2 and x+3.
The equation would be (x-2)(x+3)=0

Answer 18

I think part of your problem is that you don't really know what is meant by factors, roots, and the zero factor property.

Answer 19

im just guessing that i neeed to make em equal to 0 then multiply the expressions and keep it equaled to 0 but thanks for the help?

Answer 20

Yes. Just as I wrote:
(x-2)(x+3)=0
x^2+x-6=0
That is the polynomial equation with the given roots.