Question

How would I set this up to solve it?
Find the polynomial function with roots 1, 7, and -3 of multiplicity 2.

Answer 1

All the roots of multiplicity \(2\)?

Answer 2

And here's your example:

If you want a polynomial with root \(2\) of multiplicity \(3\),\[(x - 2)^3\]

Answer 3

so, root -3 of multiplicity 2 would be \[(x - (-3))^2\] right?

Answer 4

That is correct :-)

Answer 5

So is it only \(-3\) with multiplicity \(2\)?

Answer 6

I have no idea, the question on my homework says "Find the polynomial function with roots 1, 7, and -3 of multiplicity 2.", the teacher didn't say anything else about it.

Answer 7

so, \[(x-1) (x-7) (x-(-3))^2\] is the correct way to set it up?

Answer 8

Yes, that's correct! But if we have all those with multiplicity \(2\),\[(x - 1)^2(x - 7)^2(x + 3)^2\]

Answer 9

ok, so I'll do all of them with multiplicity of two.
\[(x-1)^2 (x-7)^2 (x-(-3))^2\] and then solve it.

Answer 10

I dunno, it's your choice. It can be either.

Answer 11

So, it becomes \[(x^2 + 1) (x^2 + 49) (x^2 + 9)\] right?

Answer 12

I think it's just \(-3\) with multiplicity of \(2\).

Answer 13

They don't usually give such hard problems.

Answer 14

oh, so then it's \[(x-1) (x-7) (x^2 + 9)\] right?

Answer 15

Hey wait, don't we have the same pics?

Answer 16

It should be
\[(x-1) (x-7) (x + 3)^2\]

Answer 17

\[(x+3)^2\ne x^2+9\]
\[(x+3)^2=x^2+2\times 3\times x+3^2\]

Answer 18

Why is OpenStudy so slow right now?

Answer 19

so, then it's \[(x-1) (x-7) (x^2 + 6x + 9)\] ?

Answer 20

thats correct, but i think you need to multiply them out for final answer, and bring it in the form, ax^4+bx^3+cx^2+dx+e

Answer 21

Yes.

Answer 22

so then the answer is \[(x^4 + 6x^3 - x^3 - 7x^3- x^2 - 7x^2 -6x - 42x - 9 - 63) \] simplified, it is \[(x^4 - 2x^3 - 8x^2 - 48x - 72)\] right?

Answer 23

Yup

Answer 24

ok, thanks!