Question

how to find zeros of –x4 + x3 + 7x2 − x − 6

Answer 1

trial and error for a root first, then use long division once you've found a root

Answer 2

but i dont know how to do tht

Answer 3

make -x^4+x^3 +7x^2 - 6 = 0, now trial and error numbers as x value see which one when subbed in, gives you 0.

Answer 4

oops i meant your equation -x^4 + x^3 + 7x^2 - x - 6 = 0

Answer 5

1 works

Answer 6

i used synthetic division to find that out

Answer 7

i mean -1

Answer 8

yes, so when x = 1, the entire equation = 0, so you could say x - 1 = 0 is a root of the equation, since the equation has a total of power 4, you can divide the equation by (x-1) and get a power 3 equation

Answer 9

ok then it's x+1 = 0

Answer 10

so (x+1) (ax^3+bx^2+cx+d) = 0

Answer 11

when your -1 works, you gotta move it to the other side of the equation to change its sign. for instance when x = -1 the whole equation = 0, moving -1 to the left by adding 1 on both sides give you x+1 = 0

Answer 12

ohok s

Answer 13

so what do you do next

Answer 14

you can use your synthetic division, or it's easier to just use long division to divide -x^4+x^3+7x^2 - x -6 by (x+1), and get your cubic equation

Answer 15

how would you solve tat with long division

Answer 16

https://www.khanacademy.org/math/algebra2/arithmetic-with-polynomials/long-division-of-polynomials/v/polynomial-division

Answer 17

@Kenshin --- ATTENTION please ! above you have wrote this :,,yes, so when x = 1, the entire equation = 0, so you could say x - 1 = 0 is a root of the equation, since the equation has a total of power 4, you can divide the equation by (x-1) and get a power 3 equation
- so than how is true ? divide by x-1 or x+1 ?

Answer 18

in this case both works, so there are 2 roots of -1 and +1, so you could in fact divide the whole equation by x^2-1 and get a much simpler quadratic quotient as a result.

Answer 19

so than you try x=-1 this is sure that you will get = zero ?

Answer 20

so i really need with this like can you write in like step after i did my synthetic divison cause i dont get it and i need help

Answer 21

so i think in case of -1 you will get 2=0

Answer 22

so what is false - or not ?

Answer 23

@Kenshin - are you here ?

Answer 24

-(-1^4) +(-1^3) +7(-1^2) - (-1) - 6
-1-1+7+1-6=0

Answer 25

That video teaches you how to do long division with algebra Janu16

Answer 26

ok

Answer 27

so can i get my 4 roots by doing long division

Answer 28

since both -1 and +1 works as roots, you will get a quadratic (ax^2+bx+c)*(x+1)*(x-1) once you divide the whole equation by x^2 - 1 yes

Answer 29

but whether it's 4 roots or 3 roots we don't know that yet, it could be a perfect square that has the curve touching a point instead of crossing it as well in that case there's a double root and those 2 roots which makes them 3 roots.

Answer 30

ok do you see how it works now? can you complete the rest?

Answer 31

yea im working

Answer 32

never learned long polynomial so having hard time so do you do x^2 times x^3?

Answer 33

no, i completed the first step for you which was:
x^2 times (x^2 - 1) [that was your 2 roots you got from (x+1)(x-1)];

and you get x^4 - x^2 to take away from your original equation, then you gotta find the next term at the top to time by (x^2 - 1) to try and cancel out the remainder, repeat this process until you reach 0

Answer 34

sorry -x^2 i meant