The sum of all non-integer roots of the equation $x^5-6 x^4+11 x^3-5 x^2-3 x+2=0$ is

If $\alpha$ and $\beta$ are the distinct roots of the equation $x^{2}+(3)^{1 / 4} x+3^{1 / 2}=0$, then the value of $\alpha^{96}\left(\alpha^{12}-\right.1) +\beta^{96}\left(\beta^{12}-1\right)$ is equal to:

Number of integral values of '$m$' for which $\{x\}^2 + 5m\{x\} - 3m + 1 < 0 $ $\forall x \in  R$, is (where $\{.\}$ denotes fractional part function)

Let $a$ be the largest real root and $b$ be the smallest real root of the polynomial equation $x^6-6 x^5+15 x^4-20 x^3+15 x^2-6 x+1=0$ Then $\frac{a^2+b^2}{a+b+1}$ 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