Sum and Product of Roots Calculator

Easily calculate the sum and product of roots for a quadratic equation of the form $$ax^2 + bx + c = 0$$. Enter the coefficients a, b, and c below to get instant results and visualize the quadratic graph.

Coefficient of $$x^2$$ (a):

Coefficient of $$x$$ (b):

Constant term (c):

Results:

Sum of Roots ($$\alpha + \beta$$):

Product of Roots ($$\alpha \beta$$):

Quadratic Equation Visualization

Understanding Sum and Product of Roots

For a quadratic equation $$ax^2 + bx + c = 0$$, if $$\alpha$$ and $$\beta$$ are the roots, then according to Vieta's formulas:

Sum of roots: $$\alpha + \beta = -\frac{b}{a}$$
Product of roots: $$\alpha \beta = \frac{c}{a}$$

These formulas provide a quick way to find the sum and product of the roots without actually solving for the roots themselves. This tool helps you calculate these values instantly and visualize the corresponding quadratic function.