Higher November 2022 Unit 1 Q21
21. Solve the following equation.
Do not use a trial and improvement method. [5]
From the formula list: The solutions of \(ax^2 + bx + c = 0\) where \(a \neq 0\) are given by \(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
| Scheme | Marks | Comments | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| \(x(4x - 5) = 2(x + 1)\) or equivalent | M1 | M1 for sight of \(x(4x - 5)\) AND \(2(x + 1)\) or equivalent | ||||||||
| \(4x^2 - 7x - 2\; [= 0]\) | A1 | Ignore presence of denominator (provided correct). | ||||||||
| \((4x + 1)(x - 2)\; [= 0]\) | B2 | B1 for \((4x \ldots\ldots 1)(x \ldots\ldots 2)\) OR for \((2x \pm 1)(2x \mp 2)\) FT their quadratic equation, provided of equivalent difficulty. | ||||||||
| \(x = -\tfrac{1}{4}\) AND \(x = 2\) | B1 | Both answers required. Strict FT ‘their derived brackets’. Allow use of quadratic formula FT their quadratic equation, provided of equivalent difficulty.
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