IntMath Home » Forum home » Polynomial Equations of Higher Degree » Find a polynomial function

IntMath forum | Polynomial Equations of Higher Degree

Find a polynomial function [Solved!]

My question

Find a polynomial function with degree 3 with real coefficients that has the given zeros:
-2, 3, -4
The polynomial function is x^(3)+?x^(2)-10x-24

Relevant page

1. Polynomial Functions and Equations

What I've done so far

Gone through your examples, but cannot find on e like it.

X

Find a polynomial function with degree 3 with real coefficients that has the given zeros:
-2, 3, -4
The polynomial function is x^(3)+?x^(2)-10x-24
Relevant page

<a href="/equations-of-higher-degree/1-polynomial-functions.php">1. Polynomial Functions and Equations</a>

What I've done so far

Gone through your examples, but cannot find on e like it.

Re: Find a polynomial function

Hi Samantha

This page has lots of useful background for you:

3. Factors and Roots of Polynomial Equations

The first example is very similar to what you need to do (but the other way round).

Show us your working (you are encouraged to use the math entry system).

X

Hi Samantha

This page has lots of useful background for you:

<a href="/equations-of-higher-degree/3-factors-roots.php">3. Factors and Roots of Polynomial Equations</a>

The first example is very similar to what you need to do (but the other way round).

Show us your working (you are encouraged to use the math entry system).

Re: Find a polynomial function

Is this what you're supposed to do?

`(x-2)(x + 3)(x -4)`

`=(x-2)(x^2-x-12)`

`=x^3-x^2-12x-2x^2+2x+24`

`=x^3-3x^2-10x+24`

So the ? mark is supposed to be `-3`, right?

X

Is this what you're supposed to do?

`(x-2)(x + 3)(x -4)`

`=(x-2)(x^2-x-12)`

`=x^3-x^2-12x-2x^2+2x+24`

`=x^3-3x^2-10x+24`

So the ? mark is supposed to be `-3`, right?

Re: Find a polynomial function

Hi Samantha

You almost got it, but fell into a common trap. Notice your `24` at the end is `+24`, but the question says `-24`?

If the zeros (aka "roots") are `-2, 3` and `4`, then the linear parts of the factored polynomial will use opposite signs, like this:

`(x+2)(x - 3)(x +4)`

`=(x+2)(x^2+x-12)`

`=x^3+x^2-12x+2x^2+2x-24`

`=x^3+3x^2-10x-24`

So the ? mark should be `3`, not `-3`.

Hope it helps.

X

Hi Samantha

You almost got it, but fell into a common trap. Notice your `24` at the end is `+24`, but the question says `-24`?
 
If the <b>zeros</b> (aka "roots") are `-2, 3` and `4`, then the linear parts of the factored polynomial will use opposite signs, like this:

`(x+2)(x - 3)(x +4)`

`=(x+2)(x^2+x-12)`

`=x^3+x^2-12x+2x^2+2x-24`

`=x^3+3x^2-10x-24`

So the ? mark should be `3`, not `-3`.

Hope it helps.

Re: Find a polynomial function

Great. I got it now.

Thanks a lot.

X

Great. I got it now.

Thanks a lot.

Reply

You need to be logged in to reply.

Search IntMath, blog and Forum