Fifth degree polynomial function

Question

Form a fifth degree polynomial function with real coefficients such that 2i, 1-3i, and 4 are real zeros and f(0)= -480

Answer 1

x= 2i

x^2 =-4

x^2 + 4=0

x=1-3i

x-1 = -3i

x^2-2x + 1 =-9

x^2 -2x +10 = 0

x=4

x-4=0

(x-4)(x^2+4)(x^2-2x+10)

= x^5 -6x4 +22x^3 -64x^2 + 72x -160

polynomial of degree 5 with real coefficients is above

but f(x) = -480 requires multiplying above by 480/160 = 3 to get

3x^5 -183x^4 +66x^3 +216x -480