Question 959031
to find an equation that has {{{x[1] = i}}}, {{{x[2] =-i}}},{{{x[3] = -4}}} and {{{x[4] =1}}} as solutions use zero product formula:

{{{f(x)=(x-x[1])(x-x[2])(x-x[3])(x-x[4])}}}

{{{f(x)=(x-i)(x-(-i))(x-(-4))(x-1)}}}

{{{f(x)=(x-i)(x+i)(x+4)(x-1)}}}

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

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

{{{f(x)=(x^2+1)(x^2+3x-4)}}}

{{{f(x)=x^2*x^2+3x*x^2-4*x^2+x^2+3x-4}}}

{{{f(x)=x^4+3x^3-4x^2+x^2+3x-4}}}

{{{f(x)=x^4+3x^3-3x^2+3x-4}}}



{{{ graph(600, 600, -10, 10, -50, 10, x^4+3x^3-3x^2+3x-4) }}}