In January, there was a suggestion Extend Square Root to Work With Floating Points?. Many of the goals from that proposal can be achieved by introducing a new exercise.
The polynomial equation 144060 x^3 - 47988 x^2 - 3211091 x + 1703680 = 0
has solutions x ≈ -4.81098, x ≈ 0.533111, x ≈ 4.61098
Students will be asked to implement a method such that
solve( [144060, -47988, -3211091, 1703680] )
will return the solutions [-4.81098, 0.533111, 4.61098]
, in any order.
Each test case polynomial will have integer coefficients, and be chosen to have 3 distinct real roots, including at least one rational root.
This allows a variety of solution methods, such as
- Newton’s method
- Cardano’s formula
- Guessing a rational root, then using the quadratic formula
- Binary chop
I don’t have a specific story suggestion. Here are some applications of cubics.