Solve for x in the equation x\(^3\) - 5x\(^2\) - x + 5 = 0
A
1, - 1, or 5
B
1, 1, or -5
C
-1, 1, or -5
D
1, 1, or 5
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
x\(^3\) - 5x\(^2\) - x + 5 = 0.
\(x^{2}(x - 5) - 1(x - 5) = 0\)
\((x^2 - 1)(x - 5) = 0 \implies (x - 1)(x + 1)(x - 5) = 0\)
\(\therefore x = 1, -1, 5\)
Source: Myschool Past Questions Archive (Record #3345)