Higher November 2022 Unit 2 Q12
12. Solve the equation \(59x^2 - 7x - 13 = 0\).
Give your answers correct to 2 decimal places.
You must 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 |
|---|---|---|
| \(x = \dfrac{-(-7) \pm \sqrt{(-7)^2 - 4 \times (59) \times (-13)}}{2 \times (59)}\) | M1 | This substitution into the formula must be seen for M1, otherwise award M0A0A0. Allow one slip in substitution for M1 only, but must be correct formula. |
| \(= \dfrac{7 \pm \sqrt{3117}}{118}\) | A1 | Can be implied from the two correct, unrounded values of \(x\), provided M1 awarded. |
| \(x\) = 0·53, \(x\) = –0·41 | A1 | CAO Both solutions required. Award SC3 for both roots correctly rounded using the trial and improvement method used correctly. |