SOLUTION: The question is: Solve x^4 - 8x^2 + 16. The possible answers are: -2, 2, -2i, 2i -2i, 2i -2, 2i -2, 2 Any help would be appreciated. Please explain in detail how you

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: The question is: Solve x^4 - 8x^2 + 16. The possible answers are: -2, 2, -2i, 2i -2i, 2i -2, 2i -2, 2 Any help would be appreciated. Please explain in detail how you      Log On


   

Question 405559: The question is:
Solve x^4 - 8x^2 + 16.
The possible answers are:
-2, 2, -2i, 2i
-2i, 2i
-2, 2i
-2, 2
Any help would be appreciated. Please explain in detail how you got to the answer. Thank you so much!
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Solving:  finding roots by setting the function = 0

x^4 - 8x^2 + 16 = 0  |note the use of ^ (uppercase 6)

factoring

(x^2 -4)(x^2 -4)= 0 

Note:SUM of the inner product(-4x^2) and the outer product(-4x^2) = -8x^2

  (x^2-4) = 0

factoring

 (x+2)(x-2) = 0  Note:SUM of the inner product(2x) and the outer product(-2x) = 0 

 (x+2)= 0   x = -2

 (x-2)= 0   x =  2