Question

find the points of intersection y=x⁴-2x+1, y=1-x^2

Answer 1

this is what i have so far

x⁴-2x+1=1-x^2

x⁴-2x+x^2=0

Answer 2

if i take out an x im left with \[x(x ^{3}+x ^{2}-2)=0\]

Answer 3

Two points of intersection.

Answer 4

there's three points

Answer 5

x(x^3+x-2)=0

Answer 6

(0,1)
and
(1,0)
and
(0,0)

Answer 7

x=0 or x^3+x-2=0
well if x=1 we see that works

1 | 1 0 1 -2
| 1 1 2
--------------------
1 1 2 | 0
so we have x^2+x+2=0
we can use quadratic formula here

Answer 8

okay i'm good now. i didnt think about that. thanks

Answer 9

i think but keep going please

Answer 10

\[x=\frac{-1 \pm \sqrt{1-4(1)(2)}}2\]
but that is not real

Answer 11

so we only have x=0 and x=1

Answer 12

why not just grapgh it?

Answer 13

what happened to your x^3

Answer 14

need to show work bass

Answer 15

if x=0 then y=1
if x=1 then y=0

Answer 16

remember i divided

Answer 17

ok i will do it on paper k?

Answer 18

what happened to you x^3

Answer 19

i divided

Answer 20

Wow, just neglect my answer. I graphed it and got the correct answers. If you don't believe it, its your loss mate.

Answer 21

but it was originally x^4

Answer 22

abe i cant just graph it thats useless. theres no way for me to show work on a calculator

Answer 23

plus i already have the answers

Answer 24

is the annswer x=0 and x=1