Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. write the polynomial in standard form. (1 point) 4, -14, and 5 + 8i

Answer 1

Since it is a polynomial
for the zero 4 you can write (x-4)
for the zero -14 you can write (x+14)
for the zero 5+8i since it is complex it will be accompanied with its conjugate 5-8i so you can write (x-(5+8i) and (x-(5-8i)) =(x^2-10x+89)
so
(x-4)(x+14)(x^2-10x+89)
expanding
x^4-67x^2+1450x-4984=0