If $\alpha,\beta,\gamma, \delta$ are the roots of $x^4-100x^3+2x^2+4x+10 = 0$ then $\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma}+\frac{1}{\delta}$ is equal to :-
$\frac{2}{5}$
$\frac{1}{10}$
$4$
$\frac{-2}{5}$
The product of all real roots of the equation ${x^2} - |x| - \,6 = 0$ is
If $72^x \cdot 48^y=6^{x y}$, where $x$ and $y$ are non-zero rational numbers, then $x+y$ equals
Let $\mathrm{S}=\left\{x \in R:(\sqrt{3}+\sqrt{2})^x+(\sqrt{3}-\sqrt{2})^x=10\right\}$. Then the number of elements in $\mathrm{S}$ is :
Let $x, y, z$ be positive reals. Which of the following implies $x=y=z$ ?
$I.$ $x^3+y^3+z^3=3 x y z$
$II.$ $x^3+y^2 z+y z^2=3 x y z$
$III.$ $x^3+y^2 z+z^2 x=3 x y z$
$IV.$ $(x+y+z)^3=27 x y z$
If $x$ is real, then the value of ${x^2} - 6x + 13$ will not be less than