Respuesta :

Given:

3 and 5i are the roots of the equation.

It is given that n=3 .

Let assume the third root be the conjugate of complex root that is -5i

Then the polynomial function :

[tex]f(x)=(x-3)(x-5i)(x+5i)[/tex][tex]f(x)=(x-3)(x^2+25)[/tex][tex]f(x)=x^3+25x-3x^2-75[/tex][tex]f(x)=x^3-3x^2+25x-75[/tex][tex]\text{The polynomial function be }f(x)=x^3-3x^2+25x-75[/tex]

Given that f(1)= -52,

[tex]f(1)=1-3+25-75[/tex][tex]f(1)=-52[/tex]