Let $x_1, x_2, \ldots, x_6$ be the roots of the polynomial equation $x^6+2 x^5+4 x^4+8 x^3+16 x^2+32 x+64=0$. Then,
$\left|x_i\right|=2$ for exactly one value of $i$
$\left|x_i\right|=2$ for exactly two values of $i$
$\left|x_i\right|=2$ for all values of $i$
$\left|x_i\right|=2$ for no value of $i$
The polynomial equation $x^3-3 a x^2+\left(27 a^2+9\right) x+2016=0$ has
The product of all real roots of the equation ${x^2} - |x| - \,6 = 0$ is
If $a$ and $b$ are the roots of equation $x^2-7 x-1=0$, then the value of $\frac{a^{21}+b^{21}+a^{17}+b^{17}}{a^{19}+b^{19}}$ is equal to $........$.
For the equation $|{x^2}| + |x| - 6 = 0$, the roots are
All the points $(x, y)$ in the plane satisfying the equation $x^2+2 x \sin (x y)+1=0$ lie on