| Exam Board | AQA |
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| Module | C1 (Core Mathematics 1) |
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| Year | 2010 |
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| Session | June |
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| Topic | Quadratic Functions |
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7
- Express \(2 x ^ { 2 } - 20 x + 53\) in the form \(2 ( x - p ) ^ { 2 } + q\), where \(p\) and \(q\) are integers.
- Use your result from part (a)(i) to explain why the equation \(2 x ^ { 2 } - 20 x + 53 = 0\) has no real roots.
- The quadratic equation \(( 2 k - 1 ) x ^ { 2 } + ( k + 1 ) x + k = 0\) has real roots.
- Show that \(7 k ^ { 2 } - 6 k - 1 \leqslant 0\).
- Hence find the possible values of \(k\).