If $x$ be real, the least value of ${x^2} - 6x + 10$ is

The roots of the equation ${x^4} - 2{x^3} + x = 380$ are

If $x$ is real and $k = \frac{{{x^2} - x + 1}}{{{x^2} + x + 1}},$ then

The number of integral values of $m$ for which the quadratic expression, $(1 + 2m)x^2 -2(1+ 3m)x + 4(1 + m),$ $x\in R,$ is always positive, is

The number of real roots of the polynomial equation $x^4-x^2+2 x-1=0$ is

Let $a$ ,$b$, $c$ , $d$ , $e$ be five numbers satisfying the system of equations

                            $2a + b + c + d + e = 6$
                            $a + 2b + c + d + e = 12$
                            $a + b + 2c + d + e = 24$
                            $a + b + c + 2d + e = 48$
                            $a + b + c + d + 2e = 96$ ,

then $|c|$ is equal to