Enter coefficients to get root sum and product fast. Export results as CSV or PDF. Learn Vieta methods with examples and clear guided steps.
| Equation | a | b | c | Sum of Roots | Product of Roots |
|---|---|---|---|---|---|
| x² - 5x + 6 = 0 | 1 | -5 | 6 | 5 | 6 |
| 2x² + 7x + 3 = 0 | 2 | 7 | 3 | -3.5 | 1.5 |
| 3x² - 12x + 9 = 0 | 3 | -12 | 9 | 4 | 3 |
| 4x² + 4x + 5 = 0 | 4 | 4 | 5 | -1 | 1.25 |
For a quadratic equation written as ax² + bx + c = 0, the roots are often called α and β.
Sum of roots: α + β = -b / a
Product of roots: αβ = c / a
Discriminant: D = b² - 4ac
Roots: x = (-b ± √D) / (2a)
These relationships come from Vieta’s formulas. They let you find the sum and product without fully expanding the roots first.
This sum and product of roots calculator helps you study quadratic equations faster. You only need the coefficients. The tool applies Vieta’s formulas directly. It returns the sum of roots and the product of roots in seconds. It also shows the discriminant and the actual roots. That makes checking your algebra easier.
The sum and product of roots reveal the structure of an equation. They help in factorization. They help in verification. They help in equation building too. Many school and college problems ask for these values without solving the full equation. This calculator supports that goal. It gives a clean answer from the standard quadratic form.
Students often use root sum and root product rules in algebra, pre calculus, and competitive exams. Teachers also use these formulas to explain coefficient relationships. This page lets you test many equations quickly. Enter positive, negative, or decimal coefficients. The tool then explains whether the roots are real, equal, or complex.
This calculator includes practical output features. You can export the result as CSV. You can also save the result as PDF. That is useful for homework files, worksheets, and revision notes. The example data table below the calculator gives a fast reference. It shows how different coefficients change the sum and product.
For any quadratic equation ax² + bx + c = 0, the sum of roots is -b/a. The product of roots is c/a. These identities are powerful because they avoid extra steps. They also make reverse problems easier. If you know the sum and product, you can often rebuild the quadratic equation. That is why this calculator is useful for both learning and solving.
It finds the sum of roots and product of roots for a quadratic equation. It also shows the discriminant, both roots, and the root type.
Use the standard quadratic form ax² + bx + c = 0. Enter the coefficients exactly as they appear in that form, including negative signs.
If a is zero, the equation is not quadratic. Vieta’s quadratic root formulas no longer apply, so the calculator asks for a nonzero a value.
Yes. The calculator accepts decimal values for a, b, and c. It then computes the sum, product, and roots using those exact numeric inputs.
Yes. If the discriminant is negative, the calculator still returns the correct sum and product. It also shows the roots in complex number form.
They help you factor equations, verify answers, and build new equations from known root relationships. They also save time in algebra and exam problems.
For ax² + bx + c = 0, the sum of roots is -b/a and the product of roots is c/a. These come from Vieta’s formulas.
Yes. Use the CSV button to export the current result as spreadsheet data. Use the PDF button to save the result block as a PDF file.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.