Question

PLEASE HELP!!!!!!!!!!!!

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

Given zeros: 2, -4, and -1 + 3i, -1 - 3i has to be another zero since complex zeros come in pairs and -1 - 3i is the complex conjugate of -1 + 3i. You get the polynomial:

f(x) = (x - 2)(x + 4)(x - (-1 + 3i))(x - (-1 - 3i))

Answer 2

but the answers they give me are
f(x) = x4 - 2x2 + 36x - 80
f(x) = x4 - 3x3 + 6x2 - 18x + 80
f(x) = x4 - 9x2 + 36x - 80
f(x) = x4 - 3x3 - 6x2 + 18x - 80

@DecentNabeel

Answer 3

Since polynomial has real coefficients, and one zero = 1+3i,
then another zero must be its conjugate: 1−3i

Zeros: 2, −4, 1+3i, 1−3i

P(x) = (x−2) (x+4) (x−(1+3i)) (x−(1−3i))
P(x) = (x−2) (x+4) ((x−1)−3i) ((x−1)+3i)
P(x) = (x−2) (x+4) ((x−1)²−9i²)
P(x) = (x−2) (x+4) ((x²−2x+1)+9)
P(x) = (x−2) (x+4) (x²−2x+10)

P(x) = (x² + 2x − 8) (x² − 2x + 10)
P(x) = x⁴ − 2x³ + 10x² + 2x³ − 4x² + 20x − 8x² + 16x − 80
P(x) = x⁴ − 2x² + 36x − 80

Answer 4

first option is the answer
@nanaruiz123

Answer 5

are you understand @nanaruiz123

Answer 6

ohh okay thank you so much @DecentNabeel

Answer 7

no problem :)