Question

PLEASE HELP !!!!

A. How many rational roots does x^4+3x^2+2=0 have?
Question options:
2
4
1
0

Answer 1

Yeah obvi. i dont no how

Answer 2

How do i find the factors ?

Answer 3

numbers that can multiply together to get another number

Answer 4

2x1=2 ?

Answer 5

So the answer is 1 or 2 ?

Answer 6

ummmm no ?

Answer 7

no

Answer 8

use rational root theorem

rational roots will be of the form \(\frac{\pm1}{1,2}\text{ so }\{-1/2,-1,1,1/2\}\) are the only possible rational roots

Answer 9

I dont know that

Answer 10

Of course lol

Answer 11

sure it does...well when someone asks for "rational roots" of a degree 4 polynomial I assume they are not meant to factor it... there is a theorem for it so I let the user know about it...you know...because its called the rational root theorem and he asked about rational roots.

Answer 12

3

Answer 13

So in short, no I am not kidding you, and in fact I was not commenting to your post.

Answer 14

correct and after checking the 4 possible ones, there are none and we are done.

Answer 15

which is SUPER easy, hence the theorem...you know....math

Answer 16

grow up

Answer 17

Math is the worst subject for me so i need all the help i can get

Answer 18

Anyone there lol @zzr0ck3r @Mertsj

Answer 19

Now im confused on what to do .-.

Answer 20

\[ x^4+3x^2+2\ge 2\]

Answer 21

And what is that !

Answer 22

You can do this quickly with a graphing calculator. Try desmos.
Type in the function, then how ever many times the graph crosses the x-axis is how many rational roots there are.

Answer 23

I am sorry he\she left you. I was simply trying to show you another way and was not meaning to interrupt. The point was that you have the information. I am not sure where you guys were heading. But I will explain the solution I was referring to.

You have a polynomial and there is a theorem that says that if \(\pm\dfrac{p}{q}\) is a rational root then p is a factor of the leading coefficient and q is a factor of the constant term.

1=1*1=-1(-1)
2=1*2=-1*-2

So the possible roots are \(-1,1,-1/2,1/2\) and you can easily check that none of these are roots. So it has none.

Answer 24

oh okay ! well that is alot easier way. thank you so muchh :)

Answer 25

you might want to look at that again @zzr0ck3r

Answer 26

Also, my way is the quickest ;)

\(x^4\ge 0\), \(3x^2\ge 0\)
thus

\[x^4+3x^2+2\ge2>0\]

thus it has no real zeros...hence no rational zeros

Answer 27

for the rational root theorem p is a factor of the constant term and q is a factor of the leading term.

Answer 28

Okay so i just need to no that right and easy way lol

Answer 29

woops sorry I had it upside down.

....q is a factor of the leading coefficient and p is a factor of the constant term.....


{1,-1,2,-2}

Answer 30

I now see you cleared that up and I am being redundant :)

Answer 31

zarkons way FTW so far imo. Takes only basic middle school math.

Answer 32

wait so whats going on ?