The sum of the squares of all the roots of the equation $x^2+|2x-3|-4=0$ is:

Let $x, y, z$ be non-zero real numbers such that $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}=7$ and $\frac{y}{x}+\frac{z}{y}+\frac{x}{z}=9$. Then,the value of $\frac{x^3}{y^3}+\frac{y^3}{z^3}+\frac{z^3}{x^3}-3$ is equal to

The population of cattle in a farm increases such that the difference between the population in year $n+2$ and that in year $n$ is proportional to the population in year $n+1$. If the populations in years $2010, 2011$ and $2013$ were $39, 60$ and $123$ respectively,then the population in $2012$ was:

The minimum value of $f(x) = \frac{x^2-2x+3}{x^2-4x+7}$ is

Let $a \in \mathbb{R}$ and let $\alpha, \beta$ be the roots of the equation $x^2+60^{\frac{1}{4}} x+a=0$. If $\alpha^4+\beta^4=-30$,then the product of all possible values of $a$ is $......$

If $\alpha, \beta$ are the irrational roots of the equation $x^5-5 x^4+9 x^3-9 x^2+5 x-1=0$,then the roots of the equation $(\alpha+\beta) x^2+2 \alpha \beta x-\alpha \beta=0$ are