Answer to Question #42982 in Calculus for shasha

Question

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

3, -13, and 5 + 4i

Answer 1

As 3, -13, 5+4i are zeros of polynomial, 5-4i is also zero. To find such polynomial write the next expression: (x-3)(x+13)(x-(5+4i))(x-(5-4i))=x^4-98x^2+800x-1599.

Answer. x^4-98x^2+800x-1599.