Question 1115284
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n value. 
n=3,
-3 and 6+5i are zeros;
f(1)=200 
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Three factors with x needed, because  degree 3, or n=3.


{{{y=a(x-h)(x-k)(x-m)}}}


You are given two of the zeros, and since complex zeros come as "conjugate pairs", you can fill in form your three given zeros.


{{{y=a(x+3)(x-(6+5i))(x-(6-5i))}}}
Simplify this, at least as far as maybe to get real number coefficients.
{{{y=a(x+3)((x-6)-5i)((x-6)+5i)}}}
{{{y=a(x+3)((x-6)^2-(25i^2))}}}
{{{y=a(x+3)(x^2-12x+36+25)}}}
{{{highlight_green(y=a(x+3)(x^2-12x+61))}}}------still in factored form, but showing only real coefficients in both factors.


Find the unknown factor, a.
{{{f(1)=200=a(1+3)(1^2-12*1+61)}}}
{{{4*(1-12+61)a=200}}}
{{{4(62-12)a=200}}}

{{{4*50a=200}}}

{{{a=200/200=1}}}-----this factor is 1.


{{{highlight(y=(x+3)(x^2-12x+61))}}}--------------the equation you want, unless you wish it multiplied further.


Use whatever graphing tool you want to.