Question 113774
find all real and imaginary roots

x^4+3x^3+x^2+4=0
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x=-2 is a root of multiplicity two.
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-2)....1....3....1....0....4
........1....1....-1....2...|..0
-2).....1....1....-1....2
.........1....-1....1...|..0

Quotient: x^2-x+1

x = [1 +- sqrt(1 - 4*1*1)]/2

x = [1 +- sqrt(-3)]/2

x = (1 + isqrt(3))/2 or x = (1 - isqrt(3))/2
or x = -2 (multiplicity 2)
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Cheers,

stan H.