Let the transformed equation of $2x^4-8x^3+3x^2-1=0$ such that the term containing the cubic power of $x$ is absent be $2x^4+bx^2+cx+d=0$. Then $b=$

If $x$ is real and $k = \frac{x^2 - x + 1}{x^2 + x + 1}$,then

If $\cos^4 \theta + \alpha$ and $\sin^4 \theta + \alpha$ are the roots of the equation $x^2 + 2bx + b = 0$,and $\cos^2 \theta + \beta$ and $\sin^2 \theta + \beta$ are the roots of the equation $x^2 + 4x + 2 = 0$,then find the value of $b$.

If the lengths of two sides of a triangle are the roots of the equation $x^2-2 \sqrt{3} x+2=0$ and the angle between these sides is $\frac{\pi}{3}$,then the perimeter of the triangle is

Let $\phi(x)=\frac{x}{(x^2+1)(x+1)}$. If $a, b$ and $c$ are the roots of the equation $x^3-3x+\lambda=0, (\lambda \neq 0)$,then $\phi(a) \phi(b) \phi(c) =$

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: