Question

WILL FAN AND GIVE MEDAL

ALGEBRA 2

What are the zeros of the function and their multiplicity? f(x)=x^4+x^3-6x^2 Show all work.

Answer 1

Solve this: x^4 +x^3 - 6x^2 = 0

Begin by factoring out x^2

By that, I mean this: x^4 +x^3 - 6x^2 = x^2 ( ? + ? + ?) = 0

@WesternBurger

Answer 2

x^2(x^2+x+6) right?

Answer 3

x^2(x^2+x-6) I meant. And then...

x^2(x+3)(x-2) so..

Are the zeros -3, 2? And multiplicity 1 for both of them?

Answer 4

@Directrix can you check my work please? I have a lot more questions to get through.

Answer 5

I just don't get what to do with the x^2 part.

Answer 6

x^2(x+3)(x-2) = 0

Use the Zero Product Property

x^2 = 0 OR x + 3 = 0 OR x-2 = 0

Answer 7

Are the zeros -3, 2? And multiplicity 1 for both of them?
YES, Those are two of the four roots. The multiplicities are correct.

Answer 8

But, what about the x^2 = 0.

From it comes x = 0 or x = 0 which is a double root.

Answer 9

Ohhhhh ok. So the answer is:

Zeros: x=-3(mult. 1), 2(mult. 1) and 0(mult. 2)

Correct?

Answer 10

Correct.

Answer 11

Thank you so much! Just one quick thing... I have a few more questions I was wondering if you could help me with? If you have the time.

Answer 12

The graph is tangent to the x axis at 0,0

Answer 13

Oh I'm not on the whole graph stuff yet lol.

Answer 14

You can close this thread and post them one per thread. A gazillion people are asking me to help but you do respond to questions so I'll try to help you.

Answer 15

Ok, so I can just tag you or something?

Answer 16

Yes.

Answer 17

Ok, thank you :)