Question

the equation 3x^6 + 4x^5 + 3x^3 - x - 3 = 0.. how many maximum possible real roots..?

can anyone show me the complete factor of this equation...?

Answer 1

what factor to divide..?

Answer 2

Oh this is not that hard. You're over thinking this.

Answer 3

actually thats what im trying to figure out..

Answer 4

The answer MUST be at least 5. Odd exponents CAN'T have imaginary roots. Right?

Answer 5

So that leaves us with the 6. Does it have imaginary roots or not? That's your only question.

Answer 6

kindly explain the process please...?

Answer 7

Well. What is the square root of 4?

Answer 8

2

Answer 9

You don's have to solve the equation - an equation can have as many roots as the degree of the equation which in this case is 6.

Answer 10

You couldn't be more wrong. It's 2 OR -2

Answer 11

This is a VERY important concept.

Answer 12

Because the cube root of 8 CANNOT be a negative. It will ALWAYS be positive. Right?

Answer 13

sorry i forgot the positive and the negative value of the square root...

Answer 14

I'm not beating you up. I just want you to take something out of this. An answer won't help you on a test, but explanations will. I'm not getting onto you by any means.

Answer 15

ok..ok.. i got the real roots now .. so another question is how do i factor it to get the value of x... in a simpler way...?

Answer 16

Well that's just it... You can't!

Answer 17

Mathematicians have proved that if a variable is raised to an nth value, it will have n answers. That does not mean that we can find all of them though.

Answer 18

****************************************
lordsampigans
Odd exponents CAN'T have imaginary roots. Right?
****************************************
Where did you get that ??

2x^3 + 3x² + 4x + 5 = 0 has roots of
-1.3711343313073632
-0.06443283434631841 + i* 1.3487610119612536
-0.06443283434631841 - i* 1.3487610119612536

Answer 19

So we have to learn different laws to work around these. Hold on now I have to debate wolf.

Answer 20

wait, wait .. answer my question first please...

Answer 21

Debate wolf??? This is a debate??????

Answer 22

Taking a square root of (-4) is what gives us an imaginary number. An imaginary number is just the EVEN root of a negative 1.

Answer 23

lol

Answer 24

An ODD root will always be just a negative answer. You will never have an imaginary number come out of an odd root.

Answer 25

I'll post a video if you don't believe me. :P

Answer 26

hey..hey.. kindly help me first please.....

Answer 27

Here this is a video for everybody to look at. https://www.khanacademy.org/math/precalculus/imaginary_complex_precalc/i_precalc/v/i-as-the-principal-root-of--1--a-little-technical

Answer 28

JnxD - it can have a maximum number of 6 roots - no further calculations to do.

Answer 29

Now back to what I was saying. If we take an even root of any number, we only have two concerns.

Answer 30

well you know what you have 3x^6 + 4x^5 + 3x^3 - x - 3 = 0
what is the highest degree

Answer 31

the highest is 6 so there is 6 roots!!

Answer 32

Guys.... Stop giving answers....Read rules. You're supposed to teach. Not spoon feed answers.

Answer 33

ok.. so what are the roots then... how do i figure out the value of the roots..?

Answer 34

well what are you guys doing then... making the learner more cconfused?

Answer 35

Let's look at the problem. We have a 3x^6.

Answer 36

lordsampigans - and what are you doing - spoon feeding confusion?

Answer 37

lol

Answer 38

This means that when we take roots of this number, we first have to worry if the number is negative. If it is, it will have an imaginary root.

Answer 39

hey... kindly help me first,.. before ur matters...please.... i thank all of u a lot.. promise...

Answer 40

then..

Answer 41

This is because of the concept I talked about earlier. sqrt of 4 is not just 2. It's 2 and -2. So a sqrt of -4 is imaginary. It technically does not exist. Does this concept make sense?

Answer 42

you can say 2i

Answer 43

Jnx - your answer is 6 - if you send me a message or just open another question - I could explain this very simply and clearly.'

Answer 44

Sqrt of 4 is saying either 2*2 or (-2)*(-2) will equal 4. But nothing multiplied by itself will equal -4. Right?

Answer 45

you might have not learned it yet but you can use i as imaginary # you learn it in algebra 2

Answer 46

so you can say 2i or -2i

Answer 47

Okay well this post is useless now. So congratulations on giving out an answer guys. You proved that you can perform math that you already know. Way to screw a student out of knowledge. Keep up the good work.

Answer 48

well i think he understand now...

Answer 49

it just depends on the degree

Answer 50

I hope so. And yes the answer is 6. Congratulations on figuring that out. Go do some MVC and then we'll be impressed.

Answer 51

yo we explained it and then gave the answer. noit just giving the answer without the explaination. the rules says to explain and then give the answer

Answer 52

that is what we did