The roots of the equation $4{x^4} - 24{x^3} + 57{x^2} + 18x - 45 = 0$, If one of them is $3 + i\sqrt 6 $, are
$3 - i\sqrt 6 , \pm \sqrt {\frac{3}{2}} $
$3 - i\sqrt 6 , \pm \frac{3}{{\sqrt 2 }}$
$3 - i\sqrt 6 , \pm \frac{{\sqrt 3 }}{2}$
None of these
If the equation $\frac{1}{x} + \frac{1}{{x - 1}} + \frac{1}{{x - 2}} = 3{x^3}$ has $k$ real roots, then $k$ is equal to -
The integer $'k'$, for which the inequality $x^{2}-2(3 k-1) x+8 k^{2}-7>0$ is valid for every $x$ in $R ,$ is
The locus of the point $P=(a, b)$ where $a, b$ are real numbers such that the roots of $x^3+a x^2+b x+a=0$ are in arithmetic progression is
Number of integers satisfying inequality, $\sqrt {{{\log }_3}(x) - 1} + \frac{{\frac{1}{2}{{\log }_3}\,{x^3}}}{{{{\log }_3}\,\frac{1}{3}}} + 2 > 0$ is
If$\frac{{2x}}{{2{x^2} + 5x + 2}} > \frac{1}{{x + 1}}$, then