If $\log _{(3 x-1)}(x-2)=\log _{\left(9 x^2-6 x+1\right)}\left(2 x^2-10 x-2\right)$, then $x$ equals
$9-\sqrt{15}$
$3+\sqrt{15}$
$2+\sqrt{5}$
$6-\sqrt{5}$
If $2 + i$ is a root of the equation ${x^3} - 5{x^2} + 9x - 5 = 0$, then the other roots are
For what value of $\lambda$ the sum of the squares of the roots of ${x^2} + (2 + \lambda )\,x - \frac{1}{2}(1 + \lambda ) = 0$ is minimum
If $\alpha , \beta $ are the roots of the equation $x^2 - 2x + 4 = 0$ , then the value of $\alpha ^n +\beta ^n$ is
The number of real solutions of the equation $|{x^2} + 4x + 3| + 2x + 5 = 0 $are
The set of all $a \in R$ for which the equation $x | x -1|+| x +2|+a=0$ has exactly one real root is: