Let \( a, b \in R \) be such that the equation \( a x^{2} - 2 b x + 15 = 0 \) has a repeated root \( \alpha \). If \( \alpha \) and \( \beta \) are the roots of the equation \( x^{2} - 2 b x + 21 = 0 \), then \( \alpha^{2} + \beta^{2} \) is equal to:
