SOLUTION: hi i have three questions and this seemed the most fitting place to put them. im very confused on these and would like to know how to solve them and what the answers are. please s

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: hi i have three questions and this seemed the most fitting place to put them. im very confused on these and would like to know how to solve them and what the answers are. please s      Log On


   

Question 1056723: hi i have three questions and this seemed the most fitting place to put them. im very confused on these and would like to know how to solve them and what the answers are.
please solve:
1) x^3 + 2x + 3 = 0
2) x^4 + 3x^2 - 4 = 0
3) (x/(x-3)) + (x/(x+3)) = (2/(x^2-9))
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x^3+2x+3. Use synthetic division
try -1
-1/1===0==2==3 remember a 0 for the x^2 term.
===1==-1==3==0
the factors are (x+1)(x^2-x+3)=0
x=-1, and by the quadratic formula will give +/- i sqrt(2) for the other 2
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3%2B2x%2B3%29%29
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x^4+3X^2-4=0. Treat this like ax^2+bx+c and factor, only there will be x^2 as leading.
(X^2+4)(X^2-1)=0
x=1,-1,+/-2i
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E4%2B3x%5E2-4%29
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(x/(x-3)) + (x/(x+3)) = (2/(x^2-9))
Multiply everything by (x^2-9) to clear the fractions.
x(x+3)+x(x-3)=2
x^2+3x+x^2-3x=2
2x^2=2
x^2=1
x=1,-1
Check roots
(1/-2)+(1/4)=2/(-8) works for 1
(1/4)+(-1/2)=2/(-8) works for -1