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what are the zeros of x^3+5x^2+5x+3

need positive negative and imaginary

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2 Answers

Won't factor.  My graphing calculator shows a curve from lower left, making an s-turn across the x and then y axis, and exiting to the upper right.  Key points include:

x-intercept:  -3.91964, 0.0

y-intercept:  0.0,3.0

Max inflection vertex:  -2.72, +6.27

Min inflection vertex:  -0.613, +1.58

You may follow the method depicted by Roman ~ 2 wks ago where the cubic is made into a depressed cubic, and solve.  The substitution of x = y - (b/3a), = y - 5/3 will eliminate the x^2 term.  This involves a lot of arithmetic which becomes tedious.  For the purist, once the real root is found, the remaining roots may be found using the quadratic formula.

Octave solves this cubic as:

-3.919, -.5401 ± .6882i