If $\sinh(\log x) = -2$,then $x =$

Let $P(x)$ be a polynomial, which when divided by $(x-3)$ and $(x-5)$ leaves remainders $10$ and $6$, respectively. If the polynomial is divided by $(x-3)(x-5)$, then the remainder is

The solution of the equation $x = \sqrt{2 + \sqrt{2 + \sqrt{2 + \dots}}}$ is:

If $\alpha$ and $\beta$ are the roots of $x^2+3(a+3)x-9a=0$ such that the roots are equal for different values of $a$ (where $\alpha > \beta$ is not applicable as roots are equal,but let $\alpha$ be the root for $a=-9$ and $\beta$ be the root for $a=-1$),then the minimum value of the expression $x^2+\alpha x-\beta$ is:

If $a, b, c$ are distinct real numbers and $a^3 + b^3 + c^3 = 3abc$,then the equation $ax^2 + bx + c = 0$ has two roots,out of which one root is

Find a polynomial $f(x)$ of degree $2$ where $f(0)=8, f(1)=12, f(2)=18$.