1MA0 Higher June 2012 Paper 2 Q22
22 Solve \(3x^2 - 4x - 2 = 0\)
Give your solutions correct to 3 significant figures. (3)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(a = 3\), \(b = -4\), \(c = -2\) \(x = \dfrac{--4 \pm \sqrt{(-4)^2 - 4 \times 3 \times -2}}{2 \times 3}\) \(= \dfrac{4 \pm \sqrt{16 + 24}}{6} = \dfrac{4 \pm \sqrt{40}}{6}\) = 1.72075922 or = – 0.3874258867 OR \(x^2 - \frac{4}{3}x - \frac{2}{3} = 0\) \(\left(x - \frac{2}{3}\right)^2 - \left(\frac{2}{3}\right)^2 - \frac{2}{3} = 0\) \(x - \frac{2}{3} = \sqrt{\left(\frac{2}{3}\right)^2 + \frac{2}{3}}\) \(x = \frac{2}{3} \pm \sqrt{\frac{10}{9}}\) | 1.72, –0.387 | 3 | M1 for \(\dfrac{--4 \pm \sqrt{(-4)^2 - 4 \times 3 \times -2}}{2 \times 3}\) (condone incorrect signs for –4 and –2) M1 for \(\dfrac{4 \pm \sqrt{40}}{6}\) or \(\dfrac{2 \pm \sqrt{10}}{3}\) A1 for one answer in the range 1.72 to 1.721 and one answer in the range – 0.387 to – 0.38743 OR M1 for \(\left(x - \frac{2}{3}\right)^2\) oe M1 for method leading to \(\frac{2}{3} \pm \sqrt{\frac{10}{9}}\) oe A1 for one answer in the range 1.72 to 1.721 and one answer in the range – 0.387 to – 0.38743 |