Question

Transforming Polynomial Functions help pleaseeee

Answer 1

Find all the zeros of the equation -3x^4+27x^2+1200=0

Answer 2

You can just graph this if you're allowed to.

Answer 3

I have to show the steps on how to do it and I don't understand it

Answer 4

Simplify it as much as possible before factoring

Answer 5

https://www.khanacademy.org/math/algebra2/polynomial_and_rational/factoring-higher-deg-polynomials/v/factoring-5th-degree-polynomial-to-find-real-zeros

Answer 6

Yes, that will help simplify the quartic function entirely :)

Answer 7

-3x^4+27x^2+1200=0
*divide by -3*
x^4-9x^2-400=0

Answer 8

Either or, actually.

Answer 9

What do I do now?

Answer 10

Now you can find two numbers that add to give you -9 and multiply to give you -400

Answer 11

hint: think of quarters.

Answer 12

I would say regular factoring is the easiest.

Answer 13

x= 4i, -4i, 5,-5

Answer 14

I have x^4-9x^2-400=0 right now and im not sure what to do next/:

Answer 15

You don't even need complex numbers, im not sure where that came from, @loveyourlife

Answer 16

What are the factors of 400? can you list them?

Answer 17

It might help if you substituted x^2 with a temporary variable to help you see the pattern better. Let a = x^2, then the equation can be rewritten as a^2-9a-400=0

Answer 18

Im so confused..

Answer 19

So you have: x^4-9x^2-400=0
Can you factor that?

Answer 20

It's like a quadratic, except the variable is x^2

Answer 21

You can rewrite the equation as (x^2)^2-9(x^2)-400=0

Answer 22

To help you see the pattern better, as a place holder, everywhere we see x^2, we'll call that 'a'.

'a' IS x^2

Answer 23

So, (x^2)^2-9(x^2)-400=0 becomes (a)^2-9a-400=0

Answer 24

Factoring, we get (a+16)(a-25)=0

Answer 25

Since a is \[x^2\]
Then, (a+16)(a-25)=0 is equivalent to \[(x^2+16)(x^2-25)=0\]

Answer 26

\[(x^2+16)(x^2-25) = (x^2+16)(x+5)(x-5)\]

Answer 27

\[(x^2+16)(x^2-25)=(x+4i)(x-4i)(x+5)(x-5)\]

Answer 28

So the roots are
\[\pm4i,\pm5\]

Answer 29

As a side note: For a polynomial of degree n, there are exactly n roots. These roots may be real or imaginary or repeated, but there are always n

Answer 30

root is another word for zero in the context of polynomials