You can put this solution on YOUR website! given the function f(x)=x^4+3x^3-6x^2+12x-40|. find all the roots of the polynomial algebraically.
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solve by rational roots theorem:
f(x)=x^4+3x^3-6x^2+12x-40
...0...|.....1.......3.......-6......12......-40......
...1...|.....1.......4.......-2......10......-30.......
...2...|.....1.......5........4......20....... 0..(2 is a root) (2 is also upper boundary)
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...0...|.....1.......5........4......20.......
..-1...|.....1......4........0......19..............
..-2...|.....1......3.......-2......16...............
..-3...|.....1......2.......-2......14.................
..-4...|.....1.....1.........0......20...................
..-5...|.....1.....0.........4.......0...(-5 is a root)
f(x)=(x-2)(x+5)(x^2+4)
roots are: -5, 2, and 2 imaginary roots(±2i)
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