Solve any quadratic equation ax² + bx + c = 0 instantly and get both real roots (if they exist). Perfect for algebra homework, physics projectile motion or graphing parabolas.
Informational calculator only. Verify important outputs independently before legal, tax, medical, engineering, safety-critical, contractual, employment, or compliance use.
Enter job values, review the estimate, then use the decision hints before ordering or quoting.
x = [-b ± √(b² - 4ac)] / (2a)The discriminant (b² - 4ac) determines the number of roots. If D > 0 — two real roots, D = 0 — one repeated root, D < 0 — no real roots.
Vertex form: y = a(x - h)² + k where h = -b/(2a)
Keep this page handy for situations where a hand calculation would be slow or easy to miscopy around quadratic axis of symmetry.
Next: quadratic discriminant.
Next: quadratic roots product.
No real roots — the equation has complex conjugate roots (e. g. , 1+2i, 1-2i). This basic calculator shows "No real roots".
Parabolas can cross the x-axis at two points, one point, or not at all, depending on the discriminant.