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Solve the equation x⁴ - 2x³ - 2x² + 2x + 1 = 0.
- x = 1, -1, 1 + sqrt(2), 1 - sqrt(2)
- x = 1, -1, (3 + sqrt(5))/2, (3 - sqrt(5))/2
- x = 1, 2, 3, -1
- x = -1, -1, 2, 3
Correct answer: x = 1, -1, 1 + sqrt(2), 1 - sqrt(2)
Solution
x = 1 and x = -1 are roots by inspection, so x² - 1 is a factor. Dividing leaves the quadratic x² - 2x - 1 whose roots are 1 +/- sqrt(2).
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