Add exception in Math::solveQuadratic() method

[KygekDev]

Introduction

The Math::solveQuadratic() method accepts parameter $a with the value 0, thus causing it to return array with invalid values (INF, NAN) if $discriminant equal to or larger than 0. Parameter $a should not pass the value 0, because in quadratic equation, coefficient a must not be 0.

Changes

Added an exception in Math::solveQuadratic() method which will be thrown if parameter $a passes the value 0.

Tests

Before adding exception:

After adding exception:

[SOF3]

Very small floats tend to lead to inaccurate results. This is a plot of log(x1), log(x2) against diminishing choices of a with the scale -log(a) (such that a = exp(-X) where X is the x-axis value):

Magnified image of the orange line without logarithm:

Mathematically, the asymptote shall converge near -0.40, but starting from 2^-30, the result becomes very unstable and eventually diverges to negative infinity (x2 converges to zero).

What I'm trying to point out is that, while a=0.0 might not mean zero (it might mean a value too small to be represented in IEEE-754-binary64), non-zero values near zero cannot yield any reasonable result anyway.

[dktapps]

A non-zero value is still technically valid regardless of the magnitude.

[SOF3]

Yes, I was just dismissing my concern when I initially thought that INF/NAN would have been valid because of precision errors. Ends up the quadratic formula messes it up really badly.

[KygekDev]

Thank you.