If $(3+i)$ is a root of $x^2+ax+b=0$,then $a=$

The number of real solutions of the equation $|x|^2 - 3|x| + 2 = 0$ is

Let $S = \{ \alpha : \log_2(9^{2\alpha-4} + 13) - \log_2(\frac{5}{2} \cdot 3^{2\alpha-4} + 1) = 2 \}$. Then the maximum value of $\beta$ for which the equation $x^2 - 2(\sum_{\alpha \in S} \alpha)^2 x + \sum_{\alpha \in S} (\alpha+1)^2 \beta = 0$ has real roots,is $...........$

The roots of the equation $x^3-3x-2=0$ are

If $\alpha \neq 0$ and $0$ are the roots of the equation $x^2 - 5kx + (6k^2 - 2k) = 0$,then $\alpha = $

$4+\frac{1}{4+\frac{1}{4+\frac{1}{4+\ldots \infty}}} = $