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