n = 3; - 5 and i are zeros; f(-3) = 60

Question

Find an nth degree polynomial function with real coefficients satisfying the given conditions.

Answer 1

This is 3rd degree polynomial.

 

f(x) = C(x + 5)(x² + 1)

 

 

Solve for C when x=-3 and f(x)=60.

Answer 2

f(x) = (x + 5)(x - i)(x + i)

f(x) = (x + 5)(x² + 1)
f(x) = x² + 5x² + x + 5

60 = a[(-3)³ + 5(-3)² +(-3) + 5]

60 = a[-27 + 45 - 3 + 5]

60 = a(20)

3 = a

f(x) = 3(x + 5)(x - i)(x + i)