Question 1178287


 Use the given zero to find all other zeros.

Zero: {{{x[1]=2i}}}=>so, you also have {{{x[2]=-2i}}}

using root product rule we have
{{{(x-x[1])(x-x[2])=(x-2i)(x-(-2i))}}}
{{{(x-x[1])(x-x[2])=(x-2i)(x+2i)}}}
{{{(x-x[1])(x-x[2])=x^2-(2i)^2}}}
{{{(x-x[1])(x-x[2])=x^2-4(-1)}}}
{{{(x-x[1])(x-x[2])=x^2+4}}}


equal given quation to zero and factor it: note one factor should be {{{x^2+4}}}

{{{0=2x^3+3x^2+8x+12}}}
{{{0=(2x^3+8x)+(3x^2+12)}}}
{{{0=2x(x^2+4)+3(x^2+4)}}}
{{{0 = (2x + 3) (x^2 + 4)}}}

=>third root is:

{{{0 (2x + 3)=0}}}=>{{{2x =-3}}}=>{{{x =-3/2}}}