How do you find all the real and complex roots of #2x^3 + 12x^2 + 50x = 0#?

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Answer 1 · 2018-03-21T09:16:09

#x=0,-3-4i" or "-3+4i#

#2x^3+12x^2+50x=0#

#hArrx^3+6x^2+25x=0#

or #x(x^2+6x+25)=0#

or #x((x^2+6x+9)+16)=0#

or #x((x+3)^2+4^2)=0#

or #x((x+3)^2-(-4^2))=0#

or #x((x+3)^2-(4i)^2)=0#

or #x(x+3+4i)(x+3-4i)=0#

Hence roots are #x=0,-3-4i" or "-3+4i#