Answer:
First function:f(x) = (20/11)*(x + 1) (x - 4) (x - 2 - 3i) (x - 2 + 3i)
Second function:f(x) = (x + 4) (x - 7 - 4i) (x - 7 + 4i)
Step-by-step explanation:
problem 1.)
nth degree : n = 4
roots -1, 4, 2 + 3i and 2 - 3i
f(1) = -120
f(x) = a*(x + 1) (x - 4) (x - 2 - 3i) (x - 2 + 3i)
f(1) = a* (1 + 1) (1 - 4) (1 - 2 - 3i) (1 - 2 + 3i) = -120
also
a*2*(-3)*(-1 - 3i) (-1 + 3i) = -120
a * -6 * ( 2 + 9) = -120
a * -6 * 11 = -120
a = -120/-66 = 20/11
so f(x) = (20/11)*(x + 1) (x - 4) (x - 2 - 3i) (x - 2 + 3i)
-------------------
n = 3
f(x) = a *(x + 4) (x - 7 - 4i) (x - 7 + 4i)
f(1) = a *(1 + 4) (1 - 7 - 4i) (1 - 7 + 4i) = 260
a * 5*( 36 + 16) = 260
a*5*52 = 260
a = 1
f(x) = (x + 4) (x - 7 - 4i) (x - 7 + 4i)