If $\alpha , \beta $ are the roots of the equation $x^2 - 2x + 4 = 0$ , then the value of $\alpha ^n +\beta ^n$ is
If $\alpha , \beta $ are the roots of the equation $x^2 - 2x + 4 = 0$ , then the value of $\alpha ^n +\beta ^n$ is
- A
${2^n}\cos \left( {\frac{{n\pi }}{3}} \right)$
- B
${2^{n + 1}}\cos \left( {\frac{{n\pi }}{3}} \right)$
- C
${2^n}\sin \left( {\frac{{n\pi }}{3}} \right)$
- D
${2^{n + 1}}\sin \left( {\frac{{n\pi }}{3}} \right)$
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