Question 1185503
 {{{n=4}}}
{{{i }}}and {{{2i}}} are zeros


first use given zeros to find polynomial

if {{{i }}}and {{{2i}}} are zeros, then we also have {{{-i }}}and {{{-2i}}} (complex zeros always come in pairs)

{{{f(x)=a(x-x[1])(x-x[2])(x-x[3])(x-x[4]) }}}......substitute zeros

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

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

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

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

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

{{{f(x)=a(x^4 + 5x^2 + 4) }}}

 
if {{{f(-2)=120}}}

{{{120=a((-2)^4 + 5(-2)^2 + 4) }}}

{{{120=a(40) }}}

{{{a=120/40 }}}

{{{a=3 }}}


{{{f(x)=3(x^4 + 5x^2 + 4) }}}

{{{f(x)=3x^4 + 15x^2 + 12 }}}