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 $\alpha ,\beta$ are the roots of $x^2 -ax + b = 0$ and if $\alpha^n + \beta^n = V_n$, then -
The least integral value $\alpha $ of $x$ such that $\frac{{x - 5}}{{{x^2} + 5x - 14}} > 0$ , satisfies
Number of natural solutions of the equation $xyz = 2^5 \times 3^2 \times 5^2$ is equal to
Let $p(x)=a_0+a_1 x+\ldots+a_n x^n$ be a non-zero polynomial with integer coefficients. If $p(\sqrt{2}+\sqrt{3}+\sqrt{6})=0$, then the smallest possible value of $n$ is