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
The number of roots of the equation $|x{|^2} - 7|x| + 12 = 0$ is
Suppose $a, b, c$ are three distinct real numbers, let $P(x)=\frac{(x-b)(x-c)}{(a-b)(a-c)}+\frac{(x-c)(x-a)}{(b-c)(b-a)}+\frac{(x-a)(x-b)}{(c-a)(c-b)}$ When simplified, $P(x)$ becomes
The number of distinct real roots of the equation $|\mathrm{x}+1||\mathrm{x}+3|-4|\mathrm{x}+2|+5=0$, is ...........
Consider the equation ${x^2} + \alpha x + \beta = 0$ having roots $\alpha ,\beta $ such that $\alpha \ne \beta $ .Also consider the inequality $\left| {\left| {y - \beta } \right| - \alpha } \right| < \alpha $ ,then
If $\alpha ,\beta $are the roots of ${x^2} - ax + b = 0$ and if ${\alpha ^n} + {\beta ^n} = {V_n}$, then