SOLUTION: find the polynomial of least degree having zeros: 8,-5 and 6i. I am so lost with this. thanks.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: find the polynomial of least degree having zeros: 8,-5 and 6i. I am so lost with this. thanks.      Log On


   

Question 591273: find the polynomial of least degree having zeros: 8,-5 and 6i.
I am so lost with this. thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x = 8, x = -5, x = 6i or x = -6i

x-8 = 0, x+5=0, x-6i, or x+6i=0

(x-8)(x+5)(x-6i)(x+6i)=0

(x-8)(x+5)(x^2-36i^2)=0

(x-8)(x+5)(x^2+36)=0

(x^2-3x-40)(x^2+36)=0

(x^2+36)(x^2-3x-40)=0

x^2(x^2-3x-40)+36(x^2-3x-40)=0

x^4-3x^3-40x^2+36x^2-108x-1440=0

x^4-3x^3-4x^2-108x-1440=0


So the polynomial that has the zeros 8, -5, and 6i is x%5E4-3x%5E3-4x%5E2-108x-1440