Roots of the algebraic equation x3 + x2 + x + 1 = 0 are
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(+ 1, + i, − i)
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(+ 1, − 1, + 1)
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(0, 0, 0)
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(− 1, + i, − i)
Reveal answer
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Correct answer
Explanation
The equation x^3 + x^2 + x + 1 = 0 can be factored as x^2(x+1) + 1(x+1) = 0, which is (x^2+1)(x+1) = 0. The roots are x = -1 and x^2 = -1, which gives x = i and x = -i.
AI explanation
By grouping the terms, the given cubic equation x^3 + x^2 + x + 1 = 0 can be factored as x^2(x + 1) + 1(x + 1) = 0. Factoring out the common binomial gives (x^2 + 1)(x + 1) = 0. Setting the first factor to zero yields x^2 = -1, which means x = +i or x = -i; setting the second factor to zero yields x = -1. Therefore, the roots of the equation are -1, +i, and -i.