4. (a) By completing the square, find in terms of \(k\) the roots of the equation $$x ^ { 2 } + 2 k x - 7 = 0 .$$ (b) Prove that, for all values of \(k\), the roots of \(x ^ { 2 } + 2 k x - 7 = 0\) are real and different.
(c) Given that \(k = \sqrt { } 2\), find the exact roots of the equation.