anonymous
  • anonymous
x^3-2x^2+5x-4=0 solve for x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
+- 1,2,4 x=2? 2 | 1 -2 5 -4 0 2 0 10 ------------ 1 0 5 6 nope, but since its all+ it aint bigger than 2
anonymous
  • anonymous
wait how'd you get 2 and 4?
amistre64
  • amistre64
x=1? 1 | 1 -2 5 -4 0 1 -1 4 ----------- 1 -1 4 0 goody (x+1)(x^2 -x +4)

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amistre64
  • amistre64
the rule is: factors of last# ------------- factors of first#
amistre64
  • amistre64
typo (x-1)(x^2 -x +4)
amistre64
  • amistre64
1,2,4 ----- leads to our options to test 1
anonymous
  • anonymous
i dont understand that
amistre64
  • amistre64
4 factors to what? 1.4 ; 2.2 all the factors of 4 are: 1,2,4
amistre64
  • amistre64
1 factors to 1 ....
anonymous
  • anonymous
?????
amistre64
  • amistre64
what is our last number in the equation?
amistre64
  • amistre64
the last number is always a product of 2 other numbers ....
amistre64
  • amistre64
1(4) = 4 2(2) = 4 thats all we get right?
anonymous
  • anonymous
sorry i dont understand that..... im only in algebra 2..... all i know is you graph it and you get x=1, then i don't know what to do from there
amistre64
  • amistre64
well, if x=1; then that means that (x-1) is a factor and you divide it out of the original equation to get whats left
anonymous
  • anonymous
yea....
anonymous
  • anonymous
but i get a remainder and i dont know what to do with it
amistre64
  • amistre64
you dont get a remainder ....
anonymous
  • anonymous
i did
anonymous
  • anonymous
when i synthetically divide i got -2 as a remainder
anonymous
  • anonymous
ooooo. i see i forgot the negative sign okay so i got a remainder of 0
anonymous
  • anonymous
then i get (x-1)(x^2-x+4) now what
amistre64
  • amistre64
x^2 -x +4 ------------------ x-1 | x^3 -2x^2 +5x -4 +x^2 ------------- -x^2 +5x - x ------ 4x -4 +4 ----- 0
anonymous
  • anonymous
then do i use the quadratic formula?
amistre64
  • amistre64
you can try; but your gonna end up with a sqrt(-) whih means it wont factor over the reals
anonymous
  • anonymous
i dont know what that is..... but do i get an imaganary number?
amistre64
  • amistre64
you get imaginary numbers yes
anonymous
  • anonymous
okay... can you help me with this? ((2)/(x+2))-((x)/(2-x))=((x^2+4)/(x^2-4))
amistre64
  • amistre64
2 x x^2+4 ---- - ---- = ------ x+2 2-x x^2-4 ^^^ -(x-2) -2 x x^2+4 ---- - ---- = ------ 2-x 2-x x^2-4 -2(2-x) x(2-x) x^2+4 ------ - ------- = ------ 4 -x^2 x^2-4
anonymous
  • anonymous
yea and then i got 4/(x+2) but i dont know how to solve for x from there
amistre64
  • amistre64
-4 +2x -2x +x^2 x^2+4 ---------------- = ------ -(x^2-4) x^2-4 4-x^2 = x^2+4 -x^2 = x^2 when x=0
amistre64
  • amistre64
that almost works :) but 1 doesnt= -1
anonymous
  • anonymous
hold on let me check my work
anonymous
  • anonymous
wait what would the answer be then?
amistre64
  • amistre64
let me do it on paper to keep better track of it
anonymous
  • anonymous
wait how'd you get -(x^2-4) in the denom. i only got (x^2-4)
anonymous
  • anonymous
when i simplify i get 4/(x+2) but i dont know what to do from there
amistre64
  • amistre64
2(2-x) -x(2+x) = x^2 +4 4 -2x -2x -x^2 = x^2+4 0 = x^2+x^2 +4x +4-4 0 = 2x^2 +4x 0 = 2x(x+2) x = 0, -2
anonymous
  • anonymous
how did you get rid of the denom.?
amistre64
  • amistre64
i multiplied evething by x^2-4; but i got an error still
anonymous
  • anonymous
.............
anonymous
  • anonymous
ok well can you just tell me how to solve 4/(x+2)
amistre64
  • amistre64
there is no solution; you end up with 0=8
anonymous
  • anonymous
how?
amistre64
  • amistre64
\[\frac{2}{x+2}-\frac{x}{2-x}=\frac{x^2 +4}{(x-2)(x+2)}\]
anonymous
  • anonymous
ok
amistre64
  • amistre64
\[\frac{2(x+2)(x-2)}{x+2} + \frac{x(x+2)(x-2)}{x+2}=x^2+4\]
anonymous
  • anonymous
shouldnt the right hand side have a denom.?
amistre64
  • amistre64
no denom, it canceled: \[frac{(x^2+4)(x-2)(x+2)}{(x-2)(x+2)}\] cancels \[2(x-2)+x(x-2)=x^2+4\] \[2x-4+x^2-2x=x^2+4\] \[x^2 -4 = x^2+4\] \[x^2-x^2 = 4+4\] \[0=8 \implies \emptyset \]
amistre64
  • amistre64
\[\frac{(x^2+4)(x−2)(x+2)}{(x−2)(x+2)}\]
anonymous
  • anonymous
ooooooo...... ok
anonymous
  • anonymous
but i dont see how it cancels on the left hand side
amistre64
  • amistre64
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anonymous
  • anonymous
omygosh thank you soooo much :)

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