Question 1125241


if the degree of a polynomial is {{{4}}}, there is four zeros

and, if the zeroes are {{{x[1]=i}}},{{{x[2]=2}}} and {{{x[3]=-2}}}, missing fourth zero is {{{x[4]=-i}}} because complex zeros always come in pairs

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

{{{f(x)=(x-i)(x-2)(x-(-2))(x-(-i))}}}

{{{f(x)=(x-i)(x-2)(x+2)(x+i)}}}

{{{f(x)=(x-i)(x+i)(x-2)(x+2)}}}

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

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

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

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

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