Question

okay so i need help with a specific part in this problem. I will medal

Answer 1

this is working with the fundamental theorem of algebra

this is the equation

\[x ^{3}-3x ^{2}+9x+13=0\]

now they gave me one of the roots. The root they gave me was

2-3i

i know that

2+3i

is the second root.

My problem is that i dont know how to find the third root.
I know this is the equation or whatever that i have to put down

(x-(2-3i)) (x-(2+3i))

the problem is that i dont know how to solve this equation to get a number or the root or whatever

Answer 2

maybe try using synthetic division? I don't know, working this out right now

Answer 3

but i dont think that applies here

Answer 4

i could be wrong though i just learned that earlier today so i need to do more with those types of problems

Answer 5

i mean i could use it for the actual equation but i dont think i can use it to find the root is what im saying

Answer 6

if no one knows its just a practice problem so hopeful theyll explain it better but theyve been doing a bad job at explaining this part so thats why i asked

Answer 7

I solved your third equation and the answer came in a quadratic equation form. It is \[x^2-4x+13\] I will apply the Quadratic forumla here, drawn below: where x^2 = a = 1. -4x = b = -4 and c =13. By applying the numbers to the Quadratic formula, the number I get it is: 2+3i.