Question

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

5, -3, and -1 + 2i
OPTIONS:

A) f(x) = x^4 - 4x^3 + 10x^2 + 20x + 75

B)f(x) = x^4 - 14x^2 - 40x - 75

C)f(x) = x^4 - 4x^3 - 10x^2 - 20x - 75

D)f(x) = x^4 + 10x^2 - 40x - 75

Answer 1

see that one zero is -1+2i hence its conjugate that is -1-2i must also be the zero of same polynomial
hence required polynomial can be calculated using
(x-5)(x+3)(x+1-2i)(x+1+2i)

Answer 2

i multiplied them but it didn't come out as any of my options… @matricked

Answer 3

check if you get D

Answer 4

=(x^2 - 2x -15 )((x+1)^2 - 4i^2)
=(x^2 - 2x -15 )(x^2+2x+1+4) as i^2=-1 rest you can multiply...

Answer 5

typo error for -15

Answer 6

Oh so it is D! Thanks!

Answer 7

yw