Question

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 @Mathematics

Answer 1

This is the answer I got: Is this correct?!?!
The zeros of a polynomial if they are complex are found as complex conjugate pairs. The polynomial has roots 4i and 5i so it cannot have any real roots. The other two roots are -4i and -5i.

The polynomial of degree 4 is

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

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

=> x^4 + 16x^2 + 25x^2 + 400

=> x^4 + 41x^2 + 400

The required polynomial is f(x) = x^4 + 41x^2 + 400

Answer 2

you are correct

Answer 3

Thanks Zarkon!