Find a polynomial function f(x) with real coefficients that has the given zeros. (There are many correct answers.) −7, −7, i

Question

Find a polynomial function f(x) with real coefficients that has the given zeros. (There are many correct answers.)

−7, −7, i

f(x)=

Answer 1

i = √-1

i² = -1

f(x) = (x + 7)(x + 7)(x - i)(x + i)

= (x² + 14x + 49)(x² + ix - ix - i²)

= (x² + 14x + 49)(x² + 1)

= x⁴ + 14x³ + 49x² + x² + 14x + 49

= x⁴ + 14x³ + 50x² + 14x + 49