5 In the equation
$$x ^ { 3 } + a x ^ { 2 } + b x + c = 0$$
the coefficients \(a , b\) and \(c\) are real. It is given that all the roots are real and greater than 1 .
- Prove that \(a < - 3\).
- By considering the sum of the squares of the roots, prove that \(a ^ { 2 } > 2 b + 3\).
- By considering the sum of the cubes of the roots, prove that \(a ^ { 3 } < - 9 b - 3 c - 3\).