JEE Main 2026 · 8 Apr · Shift 2, Mathematics question 20

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