Question

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

Answer 1

first simplify by dividing through by 3

Answer 2

in fact divide by -3

Answer 3

So would it be -x^4+9x^2+400=0?

Answer 4

which makes it easier to factor

Answer 5

x^4 - 9x^2 - 400 = 0

Answer 6

Oooh. Ok. I divided by 3 instead of -3.

Answer 7

now this will factor

Answer 8

How do I factor it?

Answer 9

it will be of the form
(x^2 + __)(x^2 - __)

Answer 10

you need to find 2 numbers whose product is -400 and whose sum = -9

Answer 11

Two numbers who sum to -9 are -4 and -5. I don't remember how to do this. I'm sorry. I feel really stupid right now.

Answer 12

factor each will help
400 = 2*2*2*2*5*5
9 = 3*3

-400 = 16 *-25

and 16 - 25 = -9

Answer 13

so we have
(x^2 - 25)(x^2+16) = 0

Answer 14

That's just what I was getting ready to say. YAY! I'm feeling a little smarter now.

Answer 15

so now you need to solve
x^2-25 = 0 and x^2 -16 = 0

Answer 16

as its a quartic equation there will be 4 zeros
2 will be real and 2 complex

Answer 17

Right now I have X^2=25 and x^2=16. Now I divide by 2 right? That way I have just x= instead of x^2= right?

Answer 18

sorry - i had one equation wrong irs x^2 + 16 = 0

Answer 19

no you take the square root of each side

Answer 20

Ooooh! Duh. Thank you. Sorry.

Answer 21

x^2 = 25
x = +/- sqrt25 = +5, -5

Answer 22

Oh! Got it! So the zeros of the equation are 5,-5, 4i, and -4i right?

Answer 23

right

Answer 24

Yay! Thank you so much! How do I give you a medal?

Answer 25

click on the blue box Best Response

Answer 26

Done. Thanks again!