If frac{1 + sqrt{3}i}{2} is a root of the equ | vedclass

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(C) Given the equation: $x^4 - x^3 + x - 1 = 0$Factor by grouping:$x^3(x - 1) + 1(x - 1) = 0$$(x^3 + 1)(x - 1) = 0$This gives two cases:$1) x - 1 = 0

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$1, -1$

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(C) Given the equation: $x^4 - x^3 + x - 1 = 0$Factor by grouping:$x^3(x - 1) + 1(x - 1) = 0$$(x^3 + 1)(x - 1) = 0$This gives two cases:$1) x - 1 = 0 \implies x = 1$$2) x^3 + 1 = 0 \implies x^3 = -1$The roots of $x^3 = -1$ are $x = -1$ and the complex roots $\frac{1 \pm \sqrt{3}i}{2}$.Thus,the roots of the equation are $1, -1, \frac{1 + \sqrt{3}i}{2}, 	ext{ and } \frac{1 - \sqrt{3}i}{2}$.The real roots are $1$ and $-1$.

If $\frac{1 + \sqrt{3}i}{2}$ is a root of the equation $x^4 - x^3 + x - 1 = 0$,then its real roots are:

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