Solve Quartic with Casio FX-115MS

[Albert Chan]

(11-29-2018 05:28 PM)Albert Chan Wrote:  Find D such that RHS is perfect square, i.e. discriminant = B^2 - 4(2D - A)(D^2 - C) = 0
We do not want complex values for E, so 2D ≥ A, D^2 ≥ C:

D ≥ max(1.5/2, √3.5625) = max(0.75, 1.904) = 1.904

A trick to force Casio FX-115MS to solve for D: 0ABC + B^2 - 4(2D - A)(D^2 - C)

D = 1.99130646 (Casio SOLVE, with guessed D = 2)

For many calculators, [SOLVE] might not be available.
We can setup Newtons iterations to get D

2 =
Ans - (B² - 4(2 Ans - A)(Ans² - C)) ÷ (8(C + Ans(A - 3 Ans
= → 1.99137931
= → 1.991306465
= → 1.99130646

Note: for Casio FX-115MS, it is not necessary to put bracket before 8
However, without the bracket, formula is ambiguous: https://plus.maths.org/content/pemdas-paradox