CALCULATOR
Positive Root of a x²+b x−q=0 Calculator
Positive Root of a x²+b x−q=0. Example: A: 1 number, B: 2 number, Q: 3 number gives 1 number. a>0,q>0 assures real roots; chosen positive root only. Bound denominator using4aq/(sqrt+b magnitude) not naive interval subtraction. Both eager branches valid; sign-switch avoids subtraction cancellation in chosen branch. Original useful product scope; historical catalog title does not grant missing mode
a>0,q>0 assures real roots; chosen positive root only. Bound denominator using4aq/(sqrt+b magnitude) not naive interval subtraction. Both eager branches valid; sign-switch avoids subtraction cancellation in chosen branch. Original useful product scope; historical catalog title does not grant missing modes or source parity. Derivation: Choose the noncancelling positive-root formula by sign of b. Every eager branch stays finite: sqrt(b²+4aq)+b = 4aq/(sqrt(b²+4aq)-b) ≥0.04/(sqrt(50000)+100)>0.00012.
Accepted inputs: A: 0.1 to 100 number; B: -100 to 100 number; Q: 0.1 to 100 number.
How the calculation works
x₊=2q/(√(b²+4aq)+b) if b≥0; otherwise (−b+√(b²+4aq))/(2a)
Worked example
With a 1 number, b 2 number, q 3 number, positive root of a x²+b x−q=0 is 1 number.
Assumptions and limits
a>0,q>0 assures real roots; chosen positive root only. Bound denominator using4aq/(sqrt+b magnitude) not naive interval subtraction. Both eager branches valid; sign-switch avoids subtraction cancellation in chosen branch. Original useful product scope; historical catalog title does not grant missing modes or source parity. Derivation: Choose the noncancelling positive-root formula by sign of b. Every eager branch stays finite: sqrt(b²+4aq)+b = 4aq/(sqrt(b²+4aq)-b) ≥0.04/(sqrt(50000)+100)>0.00012.