Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

2, -4, and 1 + 3i

Answer 1

if 1 + 3i is one root, then 1 - 3i is automatically one as well

Answer 2

since all complex roots come in conjugate pairs

Answer 3

so you really have 4 roots:

2, -4, 1 + 3i, 1-3i

Answer 4

which means

x = 2, x = -4, x = 1 + 3i, or x = 1 - 3i

x - 2 = 0, x+4 = 0, x-1 = 3i or x - 1 = -3i

x - 2 = 0, x+4 = 0, (x-1)^2 = (3i)^2 or (x - 1)^2 = (-3i)

x - 2 = 0, x+4 = 0, (x-1)^2 = 9i^2 or (x - 1)^2 = 9i^2

x - 2 = 0, x+4 = 0, (x-1)^2 = 9i^2

x - 2 = 0, x+4 = 0, (x-1)^2 = 9(-1)

x - 2 = 0, x+4 = 0, (x-1)^2 = -9

x - 2 = 0, x+4 = 0, (x-1)^2 + 9 = 0

I'll let you finish

Answer 5

Thank You :)

Answer 6

you're welcome