Homecalpro - Calculation & Material Report
Tool: Quadratic Formula Calculator — Solve ax² + bx + c = 0 | Printed on:
Mathematics & Statistics 100% Free & Privacy-First Instant Live Compute
Quadratic Formula Calculator — Solve ax² + bx + c = 0
Find real and complex roots, discriminant, and vertex coordinates of any quadratic equation.
AI Generated Visual
QUANTITATIVE PROOF
More in Mathematics & Statistics:
Quadratic Coefficients (ax² + bx + c = 0)
The Quadratic Formula
Transparent mathematical methodology explained in plain English.
x = (-b ± √(b² - 4ac)) / (2a) Finds the x-intercepts of any second-degree polynomial where a ≠ 0.
Variables Explained:
- a, b, c: Coefficients of ax² + bx + c = 0.
- b² - 4ac: The discriminant (Δ). If Δ > 0, 2 real roots; if Δ = 0, 1 root; if Δ < 0, 2 complex roots.
Real Project Example
Solving 2x² - 4x - 6 = 0
Step-by-step application of the formula.
Sample Project Inputs:
a: 2
b: -4
c: -6
Step-by-Step Calculation:
- Discriminant: (-4)² - 4(2)(-6) = 16 + 48 = 64.
- √64 = 8.
- x1 = (4 + 8) / (2 × 2) = 12 / 4 = 3.
- x2 = (4 - 8) / (2 × 2) = -4 / 4 = -1.
Calculated Answer: Roots: x = 3 and x = -1.
Knowledge Base
Frequently Asked Questions: Quadratic Formula
Click any question below to expand quick answers, formulas, and expert tips.
What happens if the discriminant is negative?
If b² - 4ac < 0, the equation has no real solutions and produces two complex conjugate roots involving the imaginary unit i.