Problem 5: Symmetrical Properties of Roots

Algebra Level 4

The roots of the quadratic equation 3x22kx+k+4=03x^2-2kx+k+4=0 are α\alpha and β\beta. If α2+β2=169\alpha^2+\beta^2=\frac{16}{9}, find the sum of all possible values of kk.

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