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

1 Answer
Mar 21, 2018

Answer:

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

Explanation:

#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#