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Solve for x in the equation x\(^3\) - 5x\(^2\) - x + 5 = 0

Mathematics
JAMB 2002

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
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Correct Answer: Option A
Explanation

x\(^3\) - 5x\(^2\) - x + 5 = 0.

\(x^{2}(x - 5) - 1(x - 5) = 0\)

\((x^2 - 1)(x - 5) = 0 \implies (x - 1)(x + 1)(x - 5) = 0\)

\(\therefore x = 1, -1, 5\)


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