4MA0 Higher January 2017 Paper 3 Q17
17 Solve the equation \(\;5x^2 + 8x - 23 = 0\)
Show your working clearly.
Give your solutions correct to 3 significant figures.
(3)
| Scheme | Marks |
|---|---|
\(\dfrac{-8 \pm \sqrt{524}}{10}\) or \(\dfrac{-8 \pm \sqrt{8^2 - -460}}{2 \times 5}\) oe or \(\dfrac{-8 \pm 2\sqrt{131}}{10}\) NB: denominator must be 2×5 or 10 and there must be evidence for correct order of operations in the numerator | M2 |
| 1.49, −3.09 | A1 |
| (3) | |
| (3 marks) |
Notes
M2: If not M2 then M1 for
\(\dfrac{-8 \pm \sqrt{8^2 - 4 \times 5 \times -23}}{2 \times 5}\)
condone one sign error in substitution;
allow partial correct evaluation
A1: for answers in range
1.489 to 1.489105 and −3.089 to −3.0891045
Award M2 A1 for answers in range
1.489 to 1.489105 and −3.089 to −3.0891045
with sufficient correct working that would gain at least M1
Alternative scheme
| Scheme | Marks |
|---|---|
| \(5\left[\left(x + \dfrac{4}{5}\right)^2 - \dfrac{16}{25}\right]\) oe | M1 |
| \(-\dfrac{4}{5} \pm \sqrt{\dfrac{23}{5} + \dfrac{16}{25}}\) oe | M1 |
| 1.49, −3.09 | A1 |
Notes
M1: for completing the square
A1: for answers in range
1.489 to 1.489105 and −3.089 to −3.0891045