| Exam Board | Edexcel |
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| Module | C1 (Core Mathematics 1) |
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| Topic | Quadratic Functions |
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4. (a) Prove, by completing the square, that the roots of the equation \(x ^ { 2 } + 2 k x + c = 0\), where \(k\) and \(c\) are constants, are \(- k \pm \sqrt { } \left( k ^ { 2 } - c \right)\).
The equation \(x ^ { 2 } + 2 k x \pm 81 = 0\) has equal roots.
(b) Find the possible values of \(k\).