Let \( \dfrac{x^2}{f(a^2+7a+3)}+\dfrac{y^2}{f(3a+15)}=1 \) represent an ellipse with major axis along \( y \)-axis, where \( f \) is a strictly decreasing positive function on \( \mathbb{R} \). If the set of all possible values of \( a \) is \( \mathbb{R}-[\alpha,\beta] \), then \( \alpha^2+\beta^2 \) is equal to:
