Higher November 2021 Unit 1 Q13
13. Solve the equation
\(4x^2 - x - 3 = 0.\)
You must use an algebraic method and show all your working. [3]
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 |
|---|---|---|
| \((4x + 3)(x - 1)\) \((=0)\) | B2 | B1 for \((4x \;\ldots\ldots\; 3)\ (x \;\ldots\ldots\; 1)\) |
| \((x =) -\tfrac{3}{4}\) AND \((x =)\ 1\) | B1 | Strict FT from their brackets provided equivalent difficulty. (Both solutions are required for this B1.) B1 if only \((x =) -\tfrac{3}{4}\) AND \((x =)\ 1\) seen. |
Alternative method (using quadratic formula)
| Scheme | Marks | Comments |
|---|---|---|
| \((x =)\ \dfrac{1 \pm \sqrt{[(-1)^2 - 4(4)(-3)]}}{2(4)}\) | M1 | Allow one error, in sign or substitution, but not in the formula for M1 A0 A0. |
| \(x = \dfrac{1 \pm \sqrt{49}}{8}\) | A1 | |
| \(x = -\tfrac{3}{4}\) AND 1 (or equivalent) | A1 |