The roots of the equation $x^{2/3} + x^{1/3} - 2 = 0$ are

The number of positive real roots of the equation $3^{x+1}+3^{-x+1}=10$ is

$\alpha, \beta, \gamma, 2, \varepsilon$ are the roots of the equation $x^5+4 x^4-13 x^3-52 x^2+36 x+144=0$. If $\alpha < \beta < \gamma < 2 < \varepsilon$,then find the value of $\alpha+2 \beta+3 \gamma+5 \varepsilon$.

For which real value of $a$ do the roots of the quadratic equation $2x^2 - (a^3 + 8a - 1) x + a^2 - 4a = 0$ have opposite signs?

The roots of the equation $x^4 - 8x^2 - 9 = 0$ are

Let $S = \{x \in \mathbb{R} : (\sqrt{3} + \sqrt{2})^x + (\sqrt{3} - \sqrt{2})^x = 10\}$. Then the number of elements in $S$ is: