If two roots of the equation ${x^3} - 3x + 2 = 0$ are same, then the roots will be
$2, 2, 3$
$1, 1, -2$
$-2, 3, 3$
$-2, -2, 1$
The equation${e^x} - x - 1 = 0$ has
Number of rational roots of equation $x^{2016} -x^{2015} + x^{1008} + x^{1003} + 1 = 0,$ is equal to
The number of pairs of reals $(x, y)$ such that $x=x^2+y^2$ and $y=2 x y$ is
Let $x, y, z$ be positive reals. Which of the following implies $x=y=z$ ?
$I.$ $x^3+y^3+z^3=3 x y z$
$II.$ $x^3+y^2 z+y z^2=3 x y z$
$III.$ $x^3+y^2 z+z^2 x=3 x y z$
$IV.$ $(x+y+z)^3=27 x y z$
Product of real roots of the equation ${t^2}{x^2} + |x| + \,9 = 0$