Question

Write a polynomial function that has a leading coefficient of 1, and the given zeros

at 3, 5, and -i.

Answer 1

9514 1400 393

Answer:

p(x) = x^4 -8x^3 +16x^2 -8x +15

Explanation:

Assuming you want real coefficients, the imaginary root means its conjugate is also a root. In factored form, the polynomial is ...

p(x) = (x -3)(x -5)(x -i)(x +i) = (x^2 -8x +15)(x^2 +1)

p(x) = x^4 -8x^3 +16x^2 -8x +15