Quadratic Positive Root
Compute the larger real solution of ax² + bx + c = 0 using the quadratic formula. The calculator validates the discriminant so you immediately know when no real positive root exists.
Ensure coefficients are correct; complex roots are not handled.
Examples
- a = 1, b = −3, c = 2 ⇒ x₊ = 2
- a = 2, b = −7, c = 3 ⇒ x₊ = 3
- a = 1, b = −5, c = 6 ⇒ x₊ = 3
FAQ
Why might the result not be positive even with the plus sign?
The “positive” label refers to the plus sign in the quadratic formula. Depending on the coefficients, the numeric result can still be negative or zero.
How do I handle floating-point rounding?
The result is displayed with up to six decimal places. If you require more precision, recompute with rational numbers or symbolic algebra tools.
What if I need both roots and their sum or product?
Use Vieta’s formulas: sum of roots = −b/a and product = c/a. Pair this calculator with the quadratic discriminant for a full picture.
Additional Information
- The quadratic formula produces two solutions: x = (−b ± √Δ) ÷ (2a); this calculator reports the solution using the plus sign.
- Δ = b² − 4ac must be nonnegative for real roots. A negative discriminant indicates complex solutions.
- If you need the smaller real root, substitute the minus sign or use a dedicated negative root calculator.