Vieta's formulas

Bounding the roots of polynomials

For the cubic polynomial P(x)=ax^3 + bx^2 + cx + d, roots x1, x2, x3 of the equation P(x)=0 satisfy:

 

The xi are roots. These formula propose picking roots one at a time, two at a time, or all three. So, as a probability spectrum, convolving this with the square root form we can make leptons conditional on spinners. The X are discrete, defined by b^[mQ].  With m small, recursive, so local inventory is available.

The X are units of the smallest Higgs quant we know of. They live in a spherical, differential world, hyperbolic world relative to quant number.  We assume Lagranian bases.  The coefficients, b,c,d are the band limits of light. So the system is composed of linear, quadratic, and cubic bases, and have difference equations along the exponent quant axis.

The finite log network is interleaved 2-ary and 3-ary. It computes the spectrum. This thing is likely in the unit circle. frequency decreases? going out from the unit circle?

In a measuring sense, the Tanh(x) gives us the grid size that maintains error bounds. Then we add whatever Hamiltonian we want to the quant system. I like the Hamiltonian of bubbles in space.