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Multiple choice

Let $\alpha, \beta$ be root of the quadratic equation $x^{2}kx+(k^{2}+2k-4)=0$, then the maximum value of $\alpha^{2}+\beta^{2}$ is equal to :

  1. $8$
  2. $\dfrac{4}{9}$
  3. $\dfrac{16}{9}$
  4. $\dfrac{8}{9}$
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