$f(x)$ is a quadratic polynomial satisfying the condition $f(x)+f\left(\frac{1}{x}\right)=f(x) f\left(\frac{1}{x}\right)$. If $f(-1)=0$, then the range of $f$ is

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

The set of all real values of $x$ satisfying the inequation $\frac{8 x^2-14 x-9}{3 x^2-7 x-6}>2$ is

When the roots of $x^3+\alpha x^2+\beta x+6=0$ are increased by 1 , if one of the resultant values is the least root of $x^4-6 x^3+11 x^2-6 x=0$, then