Relationship Between Zeroes and Coefficients

📊 Sum of Zeroes

α + β = -b/a

= -(Coefficient of x) / (Coefficient of x²)

For polynomial ax² + bx + c,
the sum of zeroes equals
negative coefficient of x divided by coefficient of x²

✖️ Product of Zeroes

αβ = c/a

= (Constant term) / (Coefficient of x²)

For polynomial ax² + bx + c,
the product of zeroes equals
constant term divided by coefficient of x²

🎯 Key Formula

ax² + bx + c = a(x - α)(x - β)

If α and β are zeroes, then:
• The polynomial can be written in factored form
• Expanding gives us the relationship formulas

🔄 Reverse Process

Given: α + β and αβ

Find: x² - (α + β)x + αβ

From sum and product, we can form the polynomial:
x² - (sum of zeroes)x + (product of zeroes)