If $\alpha , \beta , \gamma$ are roots of equation $x^3 + qx -r = 0$ then the equation, whose roots are

$\left( {\beta \gamma  + \frac{1}{\alpha }} \right),\,\left( {\gamma \alpha  + \frac{1}{\beta }} \right),\,\left( {\alpha \beta  + \frac{1}{\gamma }} \right)$

The sum of all the real values of $x$ satisfying the equation ${2^{\left( {x – 1} \right)\left( {{x^2} + 5x – 50} \right)}} = 1$  is

The set of values of $x$ which satisfy $5x + 2 < 3x + 8$ and $\frac{{x + 2}}{{x – 1}} < 4,$ is

The equation $e^{4 x}+8 e^{3 x}+13 e^{2 x}-8 e^x+1=0, x \in R$ has:

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