Which of the following are correct for any two complex numbers $z_1$ and $z_2$?

If $(2+i)$ and $(\sqrt{5}-2i)$ are the roots of the equation $(x^{2}+ax+b)(x^{2}+cx+d)=0$ where $a, b, c$ and $d$ are real constants, then the product of all the roots of the equation is

$z_1$ and $z_2$ are two complex numbers such that $|z_1 + z_2| = 1$ and $|z_1^2 + z_2^2| = 25$. Then the minimum value of $|z_1^3 + z_2^3|$ is

If $\alpha, \beta$ and $\gamma$ are angles that satisfy the following conditions, find the value of $xyz$.
$1.$ $\tan \alpha + \tan \beta + \tan \gamma = \tan \alpha \tan \beta \tan \gamma$
$2.$ $x = \cos \alpha + i \sin \alpha$
$3.$ $y = \cos \beta + i \sin \beta$
$4.$ $z = \cos \gamma + i \sin \gamma$

For a complex number $Z = a + ib$,let $\hat{Z} = b + ia$. If $Z_1$ and $Z_2$ are such complex numbers,then $\widehat{Z_1 Z_2} = $

$\cos (x + iy)$ is equal to