Question 765788
{{{f(x)= x^4 + 12x^3 - 9x^2 + 48x - 52}}}..write {{{- 9x^2}}} as {{{- 13x^2+4x^2}}}

{{{f(x)=x^4+12x^3-13x^2+4x^2+48x-52}}}....group

{{{f(x)=(x^4+4x^2)+(12x^3+48x)-(13x^2+52)}}}

{{{f(x)=x^2(x^4+4)+12x(x^2+4)-13(x^2+4)}}}

{{{f(x)=(x^2+12x-13) (x^2+4)}}}

{{{f(x)=(x^2+13x-1x-13) (x^2+4)}}}

{{{f(x)=(x-1) (x+13)(x^2+4)}}}

so, to find zeros use zero product rule:

{{{(x-1) (x+13)(x^2+4)=0}}}

if {{{x-1=0}}} => {{{x=1}}}

if {{{x+13=0}}} => {{{x=-13}}}

if {{{x^2+4=0}}} => {{{x=sqrt(-4)}}}=> {{{x=2i}}} or => {{{x=-2i}}}

so, your solutions are:{{{x=1}}},{{{x=-13}}} (real),{{{x=2i}}}, and {{{x=-2i}}} (complex)