Question 1098425
<br>If the coefficients are real and one root is 2i, then another root is -2i.<br>
Since the polynomial is degree 3, we know all the roots.<br>
The polynomial factors corresponding to the roots 3, 2i, and -2i are {{{(x-3)}}} and {{{x^2+4}}}.<br>
The polynomial is then
{{{a(x-3)(x^2+4)}}}<br>
The constant a is determined by knowing that f(-1)=20:<br>
{{{a(-1-3)(1+4) = 20}}}
{{{a(-4)(5) = 20}}}
{{{-20a = 20}}}
{{{a = -1}}}<br>
The polynomial is<br>
{{{-1(x-3)(x^2+4)}}}
or
{{{-x^3+3x^2-4x+12}}}