to graph the function and verify the real zeros and the given function value. n=3; 4 and 5 i are zeros; f(2)=-174

Question

Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing​ utility, use it to graph the function and verify the real zeros and the given function value.

n=3;

4 and 5 i are zeros;

f(2)=-174

Answer 1

The form of the polynomial is

f(x) = A(x - 4)(x - 5i)(x + 5i) = A(x - 4)(x² + 25)

with A real and A ≠ 0. Find A from setting f(2) = -174:

-174 = A(2 - 4)(2² + 25)

-174/-58=3=A

​ nth-degree polynomial function with real coefficients satisfying the given conditions

f(x)=3(x - 4)(x² + 25)