Quadratic Equations

Journey through mathematical history and master the art of solving quadratic equations!

Welcome to Quadratic Equations!

Discover the power of second-degree polynomials
and their applications through history

The Quadratic Polynomial

ax² + bx + c

Where a ≠ 0

When we set this polynomial equal to zero,
we get a quadratic equation!

🏛️ The Prayer Hall Problem

20 m
15 m
300 m²
20+x
15+2x
?
→
↓

Original Area = 300 m²

Expand: width by x, length by 2x

New Area = (20+x)(15+2x) = 300

2x² + 55x + 300 = 300

📝 Solving Step by Step

📜 Historical Journey

2000 BCE
Babylonians
300 BCE
Euclid
628 CE
Brahmagupta
820 CE
Al-Khwarizmi
870 CE
Sridharacharya

Solving Our Equation

2x² + x - 300 = 0
Using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
x = 12 or x = -12.5
Parabola: y = 2x² + x - 300
✨ The Quadratic Formula
x = (-b ± √(b² - 4ac)) / 2a

This universal formula can solve
ANY quadratic equation!

For our prayer hall problem:

x₁ = 12 meters
x₂ = -12.5 (not valid)
Click any button below to start exploring!
Choose Your Learning Path
📊 Understanding Quadratic Equations
Quadratic equations appear everywhere in nature and human constructions - from the path of thrown objects to architectural designs. Select a demonstration above to begin your mathematical journey through history!