Math
Quadratic Solver
Solve ax² + bx + c = 0 in seconds, including discriminant analysis and whether roots are real or complex.
Solve ax² + bx + c = 0 with discriminant analysis.
Quadratic formula
x = [−b ± √(b² − 4ac)] ÷ (2a)
The discriminant Δ = b² − 4ac reveals the nature of roots: Δ > 0 gives two real roots, Δ = 0 gives a repeated real root, and Δ < 0 yields complex conjugates.
How to use
- Enter coefficients a, b, and c for your quadratic equation.
- Ensure a ≠ 0; otherwise the equation is linear and cannot use the quadratic formula.
- Read the discriminant, roots, and root nature in the results panel.
Example
Input: a = 1, b = -3, c = 2
Output: Discriminant = 1, Roots = 2 and 1 (two real roots)
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Quadratic Solver: quadratic equation solver, quadratic formula calculator, quadratic solver, quadratic equation calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic. Each resource is interlinked so crawlers (and readers) can discover the next best action within a couple of clicks—one of the easiest ways to lift topical authority.
Deep dive & study plan
The Quadratic Solver is a go-to tool whenever you need to roots, discriminant, and root nature for quadratic equations.. It focuses on algebra, roots, quadratic, which means searchers often arrive with intent-heavy queries like “how to quadratic solver quickly” or “quadratic solver formula explained.” Use this calculator to capture those intents and keep learners on the page long enough to send positive engagement signals.
Under the hood, the calculator leans on the discriminant δ = b² − 4ac reveals the nature of roots: δ > 0 gives two real roots, δ = 0 gives a repeated real root, and δ < 0 yields complex conjugates.—that’s why we surface the full expression (“x = [−b ± √(b² − 4ac)] ÷ (2a)”) directly above the interactive widget. When you embed that formula inside H2s or supporting paragraphs, you help both humans and crawlers understand what entity the page represents.
Execution matters as much as the math. Follow the built-in procedure: Step 1: Enter coefficients a, b, and c for your quadratic equation. Step 2: Ensure a ≠ 0; otherwise the equation is linear and cannot use the quadratic formula. Step 3: Read the discriminant, roots, and root nature in the results panel.. Each numbered instruction is short enough to scan on mobile but descriptive enough to satisfy Google’s Helpful Content guidelines. Encourage students to jot down units, double-check signs, and compare answers with the Example card to build confidence.
The Example section itself is packed with semantic clues: “a = 1, b = -3, c = 2” leading to “Discriminant = 1, Roots = 2 and 1 (two real roots).” Pepper similar narratives throughout your copy (and internal links from related guides) so canonical search intents are answered without pogo-sticking back to Google.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Link out to at least two related calculators to keep readers exploring your topical hub.
FAQ & notes
What happens if a = 0?
The calculator treats the expression as invalid because the quadratic formula requires a non-zero a coefficient. Adjust your equation or switch to a linear solver.
How are complex roots displayed?
When the discriminant is negative, roots are shown as a conjugate pair in the form real ± imaginary·i.
What formula does the Quadratic Solver use?
The discriminant Δ = b² − 4ac reveals the nature of roots: Δ > 0 gives two real roots, Δ = 0 gives a repeated real root, and Δ < 0 yields complex conjugates.
How do I use the Quadratic Solver?
Enter coefficients a, b, and c for your quadratic equation. Ensure a ≠ 0; otherwise the equation is linear and cannot use the quadratic formula. Read the discriminant, roots, and root nature in the results panel.