Form a polynomial, f (x), with real coefficients having the given degree and zeros.

Degree: 4; zeros: 4i and 5i Form a polynomial, f (x), with real coefficients having the given degree and zeros.

Degree: 4; zeros: 4i and 5i

The question indicates that 4i and 5i are imaginary so, they cannot have real roots.

f (x) = (x - 4i) (x + 4i) (x - 5i) (x + 5i)

Then simplify it and it would look like this,

(x^2 + 16) (x^2 + 25)

Simply it again.

x^4 + 16x^2 + 25x^2 + 400 x^4 + 41x^2 + 400

The polynomial that is required is

f (x) = x^4 + 41x^2 + 400