Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

4, -8, and 2 + 5i

Answer 1

Hint: Your polynomial has to have real coefficients, so 2 + 5i can't be the only imaginary zero the function has. 2 - 5i is another zero of the function, since it is the conjugate of that imaginary zero. So you actually have 4 zeroes and your polynomial has to be of degree 4.

Answer 2

\[(x-4) (x+8)(x-(2+5 i)) (x-(2-5 i)) =x^4-19 x^2+244 x-928 \]

Answer 3

thank you! I get how you did it :)

Answer 4

Thank you for the medal.