Higher November 2019 Paper 3 Q22
22 The only solution to \(\quad x^2 + bx + c = 0 \quad\) is \(\quad x = 5\)
Work out the values of \(b\) and \(c\). [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \((x - 5)^2\) or \((5 - x)^2\) or \(x^2 - 10x + 25\ (= 0)\) or \(b = -10\) or \(c = 25\) | M1 | |
| \(b = -10\) and \(c = 25\) | A1 | |
| Alternative method 2: using \(b^2 - 4ac\) | ||
| \(b^2 - 4\ (\times 1) \times c = 0\) or \(b^2 - 4\ (\times 1) \times (-25 - 5b) = 0\) or \(b^2 + 100 + 20b = 0\) or \((b + 10)^2 = 0\) | M1 | |
| \(b = -10\) and \(c = 25\) | A1 | |
Additional guidance
Do not allow \(c = 25\) from \((x + 5)^2\) or \((5 + x)^2\)