Question 370092
If {{{i}}} and {{{4i}}} are zeros so are {{{-i}}} and {{{-4i}}}
{{{f(x)=a(x-i)(x+i)(x-4i)(x+4i)}}}
{{{f(x)=a(x^2+1)(x^2+16)}}}
.
.
Solve for {{{a}}}.
{{{f(-1)=a(1+1)(1+16)=68}}}
{{{a(34)=68}}}
{{{a=2}}}
.
.
{{{f(x)=2(x^2+1)(x^2+16)}}}
{{{f(x)=2(x^4+16x^2+x^2+16)}}}
{{{highlight(f(x)=2x^4+34x^2+32)}}}