Question

Find all the zeros of the equation

Answer 1

\[-3x^4+27x^2+1200=0\]

Answer 2

you can say: let \(\large\color{black}{ x^2=a }\) if you really don't like how \(\large\color{black}{ x^4 }\) looks.

Answer 3

Factor out -3

Answer 4

I am offering you to substitute \(\large\color{black}{ a }\) (or maybe, any other letter of your choice) is you want.

Answer 5

\[x^4-9x^2-400=0\]

Answer 6

yes, good.

Answer 7

can you factor this now?
( Hint: \(\large\color{black}{ 400=25\times16 }\) )

Answer 8

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

Answer 9

you have \(\large\color{black}{ -9x^2 }\) , not just \(\large\color{black}{ 9x^2 }\) :)

Answer 10

I meant the other way. I knew what I was trying to get hahaa. I thought I wrote it wrong
\[(x^2+16)(x^2-25)\]

Answer 11

yes, this is correct.

Answer 12

So it'll be
\[-3(x^2+16)(x^2-25)\]

Answer 13

yes, it will be \(\large\color{black}{ -3(x^2+16)(x^2-25)=0 }\)

Answer 14

Now, by a zero product property you know that:

either \(\large\color{black}{ (x^2-25)=0 }\) or \(\large\color{black}{ (x^2+16)=0 }\)

Answer 15

\[x^2-25=0\]
\[x^2=25\]
\[x=5\]

Answer 16

\[x^2+16=0\]
\[x^2=-16\]
\[x=4i\]

Answer 17

you are forgetting the \(\large\color{black}{\pm }\) s

Answer 18

I know they're there I couldn't find the sign.

Answer 19

pm

Answer 20

Oh okay
So I have
\[x= \pm 5, \pm 4i\]?

Answer 21

yes.

if you are using the equation editor, type:

pm \(\large\color{black}{\pm }\)
mp \(\large\color{black}{\mp }\)

Answer 22

you can do minus plus, with mp, if you want to:)

Answer 23

Any questions about the codes?

Answer 24

How do people get different colors? That seems to make it very helpful when explaining things

Answer 25

oh, you can insert (if you are using the equation editor, once again)

`color{red}{ } ` for example.

Answer 26

try to copy this, and put it in equation editor.
`4x+2 color{red}{-2}=10color{red}{-2}`

Answer 27

(you don't need to make it gray, just copy from the gray)

Answer 28

you want to learn how to type these codes (called latex) inside the text?

Like this \(\large\color{black}{\pm }\) ?

Answer 29

\[4x+2 \color{red}{-2}=10\color{red}{-2}\]
Awesome!
I would love to learn. I learned some coding stuff when I took a web design class. But barely remember anything given that I used a program which typed most of the coding.

Answer 30

i mean you could have been able to just use primitive ALT codes for the plus minus signs and for sigmas and on... but the question marks that these symbols become stopped me from doing this.
(Like click hold ALT, click 7 5 3 on the number pad on bottom left corner of the keyboard, release alt, and you get a plus minus sign)

Answer 31

anyways,
`It is not \(\large\color{black}{ 9 }\) `
would become:
It is not \(\large\color{black}{ 9 }\)

Answer 32

you welcome, don't want to overwhelm

Answer 33

So cool thanks!