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Alright, good sir! Allow me to help!
We need to factor this sucker, so hold on to your knickers. We have an x^4 an x^3 and an x^1 (or just x), so we need to factor using x^3 and x since we can make the x^4 through multiplication.
We have the following equation:
2x^4 - 3x^3 + 2x -4 = 0
We set the equation equal to zero so we can find when it crosses the x axis (the zeroes).
Now, we want to use our own numeral for the final number so let's move it over to the other side:
2x^4 - 3x^3 + 2x = 4
Lets try factoring this. Through some serious trial and error (not that hard, just see what you have to multiply to find this number) you can find the factors:
(x^3 + __ )*(2x + __ ) = 4 + __
I got the 2 in front of the x because I knew we needed a 2x^4.
Now, try it out and find what you need - here a 1 and -3 work:
(x^3 + 1 )*(2x - 3 ) = 4 + __
Now we need to find that number on the other side of the equation, so multiply the two out:
2x^4 - 3x^3 +2x - 3 = 4 - 3
It ended up being -3. Fun Fun.
Now lets go back to the factors and put that -3 in:
(x^3 +1)*(2x - 3) = 1
Now, we need to make this equation work and the only way this will work is if both parts on the left equal 1:
(x^3 +1) = 1 and (2x-3)=1
x^3=0 and 2x=4
x=0 and x=2
There you go! I really hope I didn't make a mistake anywhere o.o.
Wow thank you so much! I know that took a lot of time. I would give you 100 medals if I could!