SOLUTION: Which of the following is not a solution to the equation F(x)= x^5+5x^3-36x? a. 0 b. +-2 c. +-3 d.+-3i (imaginary number for i)

Algebra ->  Functions -> SOLUTION: Which of the following is not a solution to the equation F(x)= x^5+5x^3-36x? a. 0 b. +-2 c. +-3 d.+-3i (imaginary number for i)       Log On


   

Question 202854: Which of the following is not a solution to the equation F(x)= x^5+5x^3-36x?
a. 0
b. +-2
c. +-3
d.+-3i (imaginary number for i)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
By "solution" I assume you mean root (x-value that has a zero function value).

First let's factor F(x):
F%28x%29+=+x%28x%5E4+%2B+5x%5E2+-36%29
F%28x%29+=+x%28x%5E2+%2B+9%29%28x%5E2+-+4%29
F%28x%29+=+x%28x%5E2+%2B+9%29%28x+%2B+2%29%28x+-+2%29
F(x) will be zero if any of these factors are zero. If x = 0 then the first factor is zero. If x = +-3i, then the second factor is zero. If x = -2, then the third factor will be zero. If x = 2 then the fourth factor will be zero. So 0, +-3i and +-2 are all roots of F(x)

So +-3 (option (c)) are not roots of F(x).