Algebra
Solving cubic equations by trial & improvement
1. Show there is a solution to x3 = 20 between 2 and 3.
2. Show there is a solution to x3 - 30 = 0 between 3 and 4.
3. A solution to x3 + x = 50 lies between 3 and 4. Find it to 1 d.p.
4. A solution to x3 - 2x = 100 lies between 4 and 5. Find it to 2 d.p.
5. A solution to x3 + 4x + 25 lies between -3 and -2. Find it to 1 d.p.
Answers
1. 23=8 which is too small. 33=27 which is too big. So an answer must be between 2 and 3.
2. 33-30=-3 which is too small. 43-30=13 which is too big. So an answer must be between 3 and 4.
3. 3.5 gives 46.375 which is too small. 3.6 gives 50.256 which is too big. 3.55 gives 48.2888... which is too small. The answer is between 3.55 and 3.6 so it is closest to 3.6 to 1 d.p.
4. From the table we can see 4.785 is too low and 4.79 is too big so the answer must be 4.79 to 2 d.p.
| 4.5 |
82.125 |
too low |
| 4.7 |
94.423 |
too low |
| 4.8 |
100.992 |
just too big |
| 4.77 |
98.991 |
too low |
| 4.78 |
99.655 |
too low |
| 4.79 |
100.322 |
too big |
| 4.785 |
99.988 |
too low |
5. -2.5 is too low. -2.4 is too big. -2.45 is too big. The answer is between -2.5 and -2.45 so is -2.5 to 1 d.p.