Algebra
Class 10

Sum and Product of Roots

α+β=ba,αβ=ca\alpha + \beta = -\frac{b}{a}, \quad \alpha \cdot \beta = \frac{c}{a}
−50510010203040506070
Sum = -b/a, Product = c/a

Adjust Variables

Coefficient a
a =
110
Coefficient b
b =
-2020
Coefficient c
c =
-3030

For quadratic ax² + bx + c = 0, the sum of roots equals -b/a and product equals c/a. Useful for forming equations when roots are known.

Real-World Applications

Symmetric functions — Calculating expressions like α² + β² = (α+β)² - 2αβ without finding individual roots.

Forming equations — Creating a quadratic equation when given sum and product of required solutions.

Vieta's formulas application — Extending to higher degree polynomials for competitive exams.

Error checking — Verifying calculated roots by checking sum and product conditions.

Physics problems — When two times satisfy a condition (up and down for projectile), their product relates to height.

Circuit analysis — Finding resonant frequencies where product and sum of roots matter.

Economics — Equilibrium price calculations in supply-demand models.

Polynomial division — Simplifying expressions using root relationships.

Cryptography — Some encryption algorithms use polynomial root properties.

Game theory — Nash equilibrium calculations in two-player scenarios.

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