Mathematician Finds Easier Way to Solve Quadratic Equations

[Albert Chan]

(05-04-2024 07:37 PM)Gerson W. Barbosa Wrote:  \(x_{1}=\left({\cos\left({\arcsin{\frac{\sqrt{q}}{-\frac{p}{2}}}}\right)+1}\right)\times-\frac{p}{2}\)

Going for x²+p*x+q=0 big root ... I like it!

cos(asin(z)) = √(1-z²)      // both sides have non-negative real part

x1 = (√(1 - q/(-p/2)²) + 1) * -p/2
x2 = q/x1

Another way to see this:

x^2 + p*x + q = 0            // x = (-p/2)*y
y^2 - 2y + sin(θ)^2 = 0    // sin(θ)^2 = q/(-p/2)^2
(y-1)^2 = cos(θ)^2
y = 1 ± cos(θ)