The equation $\sqrt {3 {x^2} + x + 5} = x - 3$ , where $x$ is real, has

If $2 + i$ is a root of the equation ${x^3} - 5{x^2} + 9x - 5 = 0$, then the other roots are

Let $a$ , $b$ , $c$ are roots of equation $x^3 + 8x + 1 = 0$ ,then the value of 

 $\frac{{bc}}{{(8b + 1)(8c + 1)}} + \frac{{ac}}{{(8a + 1)(8c + 1)}} + \frac{{ab}}{{(8a + 1)(8b + 1)}}$ is equal to

If two roots of the equation ${x^3} - 3x + 2 = 0$ are same, then the roots will be

If $x$ be real, then the minimum value of ${x^2} - 8x + 17$ is

The number of distinct real roots of the equation $x ^{7}-7 x -2=0$ is