Question

What is a quartic function with only the two real zeroes given?
x = –1 and x = –3

Answer 1

You can go with (x + 1)^2 times (x + 3)^2

The reason this works is that it will give you a x^4 term and you still have only the 2 roots.

Roots are of the form:

(x - root) for you factors.

Answer 2

So, basically you have both roots twice, so that's why each factor has a 2 on it for an exponent.

Answer 3

You could also have put a 3 on one of them and left the other root as a single power (no exponent)

Answer 4

Is this making sense to you?

Answer 5

I am lost completely

Answer 6

np, I'll give you a little more detail:

First off, a quartic polynomial function has as its highest exponent, an x^4 term. That means that if you have an equation of the form:

y = (x - root1)(x - root2)(x - root3)(x - root4)

you will have quartic function. But we can have only 2 different roots, so a good choice is to have root1 twice and root 2 twice:

y = [(x - root1)^2][(x - root2)^2]

Answer 7

That's the same as:

y = (x - root1)(x - root1)(x - root2)(x - root2)

which also has root1 twice and root2 twice. It's just writing out the factors without the exponents. This equation will give you 0 for "y" if you replace x with either root, which is what you want to solve this problem.

Answer 8

And to finish this off, you are given x = -1 and x = -3 as the only 2 roots you can have. And since the factor to give "0" using the root is:

(x - root)

one factor is [x - (-1)] which is (x + 1)
the other is [x - (-3)] which is (x + 3)

So, your polynomial is:

y = (x + 1)(x + 1)(x + 3)(x + 3)

Answer 9

You have other choices, but the above polynomial works. You could also have:

y = (x + 1)(x + 3)(x + 3)(x + 3)

or

y = (x + 1)(x + 1)(x + 1)(x + 3)

Both of those are quartics having only 2 different roots.

That should make it all clearer now. Now are you good on this?

Answer 10

Here's a graph of the first solution

Answer 11

sorta so which one would it be?
y = x4 – 4x3 – 4x2 – 4x – 3
y = –x4 + 4x3 + 4x2 + 4x + 3
y = x4 + 4x3 + 3x2 + 4x – 4
y = x4 + 4x3 + 4x2 + 4x +3
I understand how you did that i just don't know which one it will be.

Answer 12

@tcarroll010

Answer 13

I didn't know that you had choices. That changes the whole way you approach this problem. You can solve it 2 ways that I know of. The first way rst and the best and fastest is to perfrom synthetic division on each choice until you hit upon the choice that has only those 2 roots.

Answer 14

Number #1 is out because -1 is not a root. So, I eliminated that one so far.

Answer 15

Number 2 is out because it also has +1 as a root.

Answer 16

Are you sure you wrote those choices down correctly?

Answer 17

I actually copied and paste so yeah

Answer 18

And the roots are supposed to be -1 and -3 ?

Answer 19

yeah that is why i couldn't figure it out. That is what confused me

Answer 20

It looks like like the last one works. I tried it again.

Answer 21

okay thanks again

Answer 22

you're welcome.