Question

Someone help! Write a function with the given characteristics. A polynomial with rational coefficients having roots 4 and 3-i

Answer 1

@jim_thompson5910 can you help?

Answer 2

Hopefully you agree that if 3-i is one root, another root is 3+i, right?

Answer 3

yes i agree wch would make our roots 4 , 3-i , and 3+i right?

Answer 4

@jim_thompson5910

Answer 5

if 4 is a root, then do you agree that x-4 is a factor?

Answer 6

yes

Answer 7

if 3+i and 3-i is a root, then what must the factor be? any idea?

Answer 8

3?

Answer 9

If 3+i is a root, then...
x = 3+i
x - 3 = i
(x - 3)^2 = i^2
(x - 3)^2 = -1
(x - 3)^2 + 1 = 0


Hopefully you see how if 3+i is a root, then (x - 3)^2 + 1 is factor

Answer 10

ok

Answer 11

agreed? or no?

Answer 12

yes i agree

Answer 13

so we have these two factors

(x-4) and ((x - 3)^2 + 1)

Answer 14

(x - 3)^2 + 1 is the same as x^2-6x+9+1 = x^2-6x+10

Answer 15

would we end up FOIL them?

Answer 16

so you need to multiply out (x-4) and (x^2-6x+10)

Answer 17

would it be x^3-10x^2+34x-40

Answer 18

that is the correct answer

Answer 19

so that would be the final answer?

Answer 20

yes