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

Question

n=4;

i and 2i are zeros;

f(-1)=30

Answer 1

f(x) =3x⁴ +15x²+12 is the 4th degree polynomial with the given imaginary zeros

i and 2i are two zeros

-i and -2i are the other two zeros

they come in conjugate pairs

that's the lowest degreed polynomial. There are higher powered polynomials with those 4 zeros, an infinite number of higher powered polynomials