How to use the quadratic equation from roots calculator
Build the quadratic equation with given roots, in the form x² + bx + c = 0. Enter root 1, root 2 in the fields above; the coefficient b, constant c, equation are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “quadratic from roots”, “equation with roots”, “factor to quadratic”, “calculate quadratic equation from roots”, “find coefficient b”.
Formula
Variables
- r1 — Root 1
- r2 — Root 2
Worked example
With root 1 = 2, root 2 = -5, the calculator gives coefficient b ≈ 3; constant c ≈ -10; equation ≈ x² + 3x - 10 = 0 text.
Frequently asked questions
What is the quadratic equation from roots calculator used for?
Build the quadratic equation with given roots, in the form x² + bx + c = 0. It helps with questions such as “quadratic from roots”, “equation with roots”, “factor to quadratic”.
What is the formula for the quadratic equation from roots calculation?
Coefficient b = -(r1+r2). Constant c = r1 × r2. Equation (text) = "x² "+(-(r1+r2)>=0?"+ ":"- ")+abs(r1+r2)+"x "+(r1 × r2>=0?"+ ":"- ")+abs(r1 × r2)+" = 0". Here r1 is root 1, r2 is root 2.
What inputs do I need for the quadratic equation from roots calculator?
You need root 1, root 2. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the quadratic equation from roots calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the quadratic equation from roots result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.