Question

Solve the equation:
x^4-x^3-x^2-x-2=0

Answer 1

You may try to spot roots by eye or by the rational roots theorem to begin...

Answer 2

yes, but it isn't easy :(

Answer 3

Do you know rational roots theorem?

Answer 4

unfortunately not :(

Answer 5

OK, if you have a polynomial ax^n+....+c then possible rational roots are given by plus/minus factor combinations of c/a

In this case, 2/1 so 1/1, -1/1, 2/2, -2/2 so you shoudl first check plus minus 1 and 2

(actually it is a good idea to check plus minus 1 anyway)

Answer 6

may i suggest a way to find one of the roots easily:
The rule below will help in determining whether x=1 and/or x=-1 is a root of the equation or not:
1.Find the sum of coefficients of odd power terms(coefficients of x^3 and x here)
2.Find the sum of coefficients of even power terms(coefficient of x^4,x^2 and constant)
If these two are equal then (x=−1) is the root and (x+1) is the factor.
If the sum of these two=0, then (x=1) is the root and (x−1) is the factor.
Once we get x=+1 and/or x=-1 as roots we can always do synthetic division or divide the given polynomial by (x±1)

Answer 7

so how it should be write ?
x^4-1-x^3+1-x^2+1-x+1?

Answer 8

x^4-x^3-x^2-x-2=0

(-1)^4 -(-1)^3 -(-1)^2 - (-1) -2 = 0 is true so x = -1 works

If you test 2, you will find that works as well.

So then you have (x+1)(x-2)(quadratic) = 0 left to solve which is not too hard.

Answer 9

to get the quadratic, u need to do synthetic division or long division of polynomials.

Answer 10

by dividing given polynomial by x+1 and then x-2

Answer 11

but how did you this (x+1)(x-2)(quadratic) = 0 ?

Answer 12

I wrote it above??

Answer 13

ok, but how i should to know that 1 is good ?

Answer 14

sorry -1 ?

Answer 15

What I wrote:

"(-1)^4 -(-1)^3 -(-1)^2 - (-1) -2 = 0 is true so x = -1 works"

Answer 16

so i must count for 0, 1, -1 and looking for a good number?

Answer 17

Again, what I wrote:

"OK, if you have a polynomial ax^n+....+c then possible rational roots are given by plus/minus factor combinations of c/a

In this case, 2/1 so 1/1, -1/1, 2/2, -2/2 so you shoudl first check plus minus 1 and 2

(actually it is a good idea to check plus minus 1 anyway)"

Answer 18

ok,now i understand :) thank you very very much :)

Answer 19

ur welcome

Answer 20

:)