If $\alpha, \beta$ are the roots of the equation $x^2-2 x+4=0$ and for any $n \in \mathrm{N},…

If $\alpha, \beta$ are the roots of the equation $x^2-2 x+4=0$ and for any $n \in \mathrm{N}, \alpha^n+\beta^n=k \cos \frac{n \pi}{3}$ then $k=$
  1. $2^n$
  2. $2^{n+1}$
  3. $2^n-1$
  4. $2^n+1$

Solution

No solution. Refer to answer key.

Asked in: AP EAMCET 2017 (24 Apr Shift 1)

Practice more Quadratic Equation questions on Aicharya