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}$
If $\alpha ,\beta ,\gamma $are the roots of the equation ${x^3} + x + 1 = 0$, then the value of ${\alpha ^3}{\beta ^3}{\gamma ^3}$
Let $a, b, c, d$ be real numbers such that $|a-b|=2$, $|b-c|=3,|c-d|=4$. Then, the sum of all possible values of $|a-d|$ is
For the equation $|{x^2}| + |x| - 6 = 0$, the roots are
If $\alpha, \beta$ are roots of the equation $x^{2}+5 \sqrt{2} x+10=0, \alpha\,>\,\beta$ and $P_{n}=\alpha^{n}-\beta^{n}$ for each positive integer $\mathrm{n}$, then the value of $\left(\frac{P_{17} P_{20}+5 \sqrt{2} P_{11} P_{19}}{P_{18} P_{19}+5 \sqrt{2} P_{18}^{2}}\right)$ is equal to $....$
If the sum of two of the roots of ${x^3} + p{x^2} + qx + r = 0$ is zero, then $pq =$