SOLUTION: Find all roots of the polynomial x^3-x^2+16x-16. My answer is -1,4i,-4i is this right. thanks for looking at this problem.

Algebra ->  Radicals -> SOLUTION: Find all roots of the polynomial x^3-x^2+16x-16. My answer is -1,4i,-4i is this right. thanks for looking at this problem.      Log On


   

Question 43924This question is from textbook Algebra and Trigonometry with Analytic Geometey
: Find all roots of the polynomial x^3-x^2+16x-16. My answer is -1,4i,-4i is this right. thanks for looking at this problem. This question is from textbook Algebra and Trigonometry with Analytic Geometey

Found 2 solutions by longjonsilver, tutorcecilia:
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
the 3 roots are +1, 4i and -4i.

If you put +1 into the polynomial, you get zero. If you put -1 into it, you get -34.

Well done on the complex roots though.

jon

Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
x^3-x^2+16x-16
What I did was first set the equation equal to zero and than factored:
x^3-x^2+16x-16=0
x^2(x-1) + 16(x-1) = 0
Re-group the terms and set each factor equal to zero:
(x^2+16)(x-1)=0
x^2+16=0
x^2=-16
x=+-4i
.
x-1=0
x=+1