Question

Form a polynomial whose zeros and degrees are given. Do not simplify.

Zeros: 3; multiplicity 2;-3, multiplicity 2; degree 4

Answer 1

do you know how to start?

Answer 2

I have no idea. I'm new to this. I do know that the first x value will have an exponent of 4.

Answer 3

yes that is correct. you can start by writing down a generic polynomial in a "factorized" form: \[(x-a)(x-b)(x-c)(x-d)=0\]

Answer 4

this is polynomial of 4th order, right? (you can always check that by multiplying out the terms and see that you will get an exponent of 4 on the highest term)

Answer 5

a, b, c, and d are the zeros of this polynomial, that is, at these values of x the total polynomial will always become 0. Does this make sense?

Answer 6

Yes. But this problem only has 3 zeros

Answer 7

the way i understand the problem is that there is one zero at 3 with multiplicity 2, and then another zero at -3 with multiplicity 2.

Answer 8

together that will give you order of four (2xmultiplicity of2)

Answer 9

How do i write an equation from all that information?

Answer 10

so you take the first zero (3) and put it as a and b (because the multiplicity 2), then you set c and d to -3 (again because multi is 2)

Answer 11

so the equation becomes \[(x-3)(x-3)(x+3)(x+3)=0\]

Answer 12

And then do I multiply it out?

Answer 13

you can now check that if you set x=3 the polynomial will get you 0, same for -3

Answer 14

yes you multiply it out!

Answer 15

And thats the polynomial, correct?

Answer 16

correct!

Answer 17

Thank you!

Answer 18

no prob!

Answer 19

feel free to paste your result i can double check