Question

Find a polynomial function with real coefficients that has 3 and -2 i as its roots.
a. x3 - 3x2 + 4x - 12
b. x3 + 3x2 + 4x + 12
c. x3 + 3x2 - 4x - 12
d. x3 - 3x2 - 4x + 12

Answer 1

If -2i is a root, then 2i has to be one too.

Answer 2

So if a root of a function (x-r) is r, then we should negate all the roots and pair them with an x.

Answer 3

Like this: roots are 3, 2i, -2i, so negatives are -3, -2i, 2i, so binomials are (x-3)(x-2i)(x+2i).

Answer 4

multiply out and get
\[(x-3)(x^2+4)\] and then multiply again

Answer 5

x=3? I'm thinking either a. or c....

Answer 6

\[(x-3)(x^2+4)=x^3-3 x^2+4 x-12\]

Answer 7

Thank you satellite73!