Solve Quartic with Casio FX-115MS
09-02-2019, 02:35 PM (This post was last modified: 09-02-2019 02:37 PM by Albert Chan.)
Post: #6
 Albert Chan Senior Member Posts: 2,356 Joined: Jul 2018
RE: Solve Quartic with Casio FX-115MS
(08-30-2019 02:02 PM)Albert Chan Wrote:  An old algorithm for solving Quartics: Brown's method ...

c^2 - A c + (B-Y) = 0
d^2 - Y d + D = 0

Step 3: make sure roots, c1 d2 + c2 d1 = C. If not, swap d1, d2 ...

Calculate AY/2
If AY/2 > C, make sure roots of c,d sorted the same way
If AY/2 < C, make sure roots of c,d sorted opposite way

To show AY/2 trick work, let roots, [c1,c2] = [p+q, p-q], [d1,d2] = [r+s,r-s]

C = c1 d2 + c2 d1
= (p+q)(r-s) + (p-q)(r+s)
= (pr - ps + qr - qs) + (pr + ps - qr - qs)
= 2pr - 2qs
= 2(A/2)(Y/2) - 2qs
= AY/2 - 2qs

If AY/2 = C, then 2qs = 0, sort order does not matter.
If AY/2 > C, then 2qs > 0, thus c,d roots sorted the same way.
If AY/2 < C, then 2qs < 0, thus c,d roots sorted opposite way.
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 Messages In This Thread Solve Quartic with Casio FX-115MS - Albert Chan - 11-29-2018, 05:28 PM RE: Solve Quartic with Casio FX-115MS - Albert Chan - 11-29-2018, 10:31 PM RE: Solve Quartic with Casio FX-115MS - Albert Chan - 02-04-2019, 01:39 PM RE: Solve Quartic with Casio FX-115MS - Albert Chan - 08-24-2019, 12:47 PM RE: Solve Quartic with Casio FX-115MS - SlideRule - 03-14-2020, 01:28 AM RE: Solve Quartic with Casio FX-115MS - Albert Chan - 08-30-2019, 02:02 PM RE: Solve Quartic with Casio FX-115MS - Albert Chan - 09-02-2019 02:35 PM RE: Solve Quartic with Casio FX-115MS - Albert Chan - 02-01-2020, 12:27 PM RE: Solve Quartic with Casio FX-115MS - Albert Chan - 03-13-2020, 06:30 PM

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