The roots of the equation ${x^4} - 2{x^3} + x = 380$ are
$5, - 4,\frac{{1 \pm 5\sqrt { - 3} }}{2}$
$ - 5,4, - \frac{{1 \pm 5\sqrt - 3}}{2}$
$5,4,\frac{{ - 1 \pm 5\sqrt - 3}}{2}$
$ - 5, - 4,\frac{{1 \pm 5\sqrt - 3}}{2}$
The number of real roots of the equation ${e^{\sin x}} - {e^{ - \sin x}} - 4$ $ = 0$ are
Let $x$ and $y$ be two $2-$digit numbers such that $y$ is obtained by reversing the digits of $x$. Suppose they also satisfy $x^2-y^2=m^2$ for some positive integer $m$. The value of $x+y+m$ is
The number of integers $a$ in the interval $[1,2014]$ for which the system of equations $x+y=a$, $\frac{x^2}{x-1}+\frac{y^2}{y-1}=4$ has finitely many solutions is
If $x$ is real, then the maximum and minimum values of expression $\frac{{{x^2} + 14x + 9}}{{{x^2} + 2x + 3}}$ will be
If $\alpha ,\beta ,\gamma$ are the roots of $x^3 - x - 2 = 0$, then the value of $\alpha^5 + \beta^5 + \gamma^5$ is-