Mathematician Finds Easier Way to Solve Quadratic Equations

[Gerson W. Barbosa]

(05-06-2024 02:32 AM)Albert Chan Wrote:  

(05-06-2024 12:23 AM)Gerson W. Barbosa Wrote:  The accuracy of the second root can be improved simply by calculating it as x₂ = q/x₁

x1 = -p/2 + √Δ
x2 = q/x1

Not an improvement.
Depends on sign(Re(p)), we have 50:50 chance is getting both good roots, or both bad!

I was aware of that. That’s why I added “assuming of course that the first root is accurate enough”. No problem with the few examples I tried, though. Perhaps I need a more comprehensive list of examples to check. Considering the possibilities you mention, I think it’s better to compute the second root as x₂ = -(b + x₁). At least divisions by zero are completely avoided.