Intermediate November 2016 Unit 2 Q13
13. A solution to the equation
\[2x^3 - 3x - 17 = 0\]lies between 2 and 3.
Use the method of trial and improvement to find this solution correct to 1 decimal place.
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| One correct evaluation 2 ≤ x ≤ 3 | B1 | |
| 2 correct evaluations 2·15 ≤ x ≤ 2·35, ( one value < 0, one value > 0.) | B1 | |
| 2 correct evaluations 2·25 ≤ x ≤ 2·35, ( one value < 0, one value > 0.) | M1 | |
| x = 2·3 | A1 |
Correct evaluation regarded as enough to identify if negative or positive. If evaluations not seen accept ‘too high’ or ‘too low’.
| x | 2x3 – 3x – 17 | ||
|---|---|---|---|
| 2 | –7 | ||
| 2·1 | –4·778 | ||
| 2·2 | –2·304 | ||
| 2·3 | 0·434 | 2·15 | –3·573... |
| 2·4 | 3·448 | 2·25 | –0·968... |
| 2·5 | 6·75 | 2·26 | –0·693... |
| 2·6 | 10·352 | 2·27 | –0·415... |
| 2·7 | 14·266 | 2·28 | –0·135... |
| 2·8 | 18·504 | 2·29 | 0·147... |
| 2·9 | 23·078 | 2·35 | 1·905... |
| 3 | 28 |