🎯 Chapter: Quadratic Equations
🔹 1. What is a Quadratic Equation?
👉 Standard form:
A quadratic equation is an equation of degree 2.
👉 Example:
ax² + bx + c = 0
🔹 2. Types of Quadratic Equations
x² + 5x + 6 = 0
Complete → x² + 5x + 6 = 0
🔹
Incomplete → x² – 9 = 0
👉
3. Factorization Method
Example:
👉
x² + 5x + 6 = 0
👉
Factors of 6 = 2, 3
👉
x² + 2x + 3x + 6 = 0
👉
x(x + 2) + 3(x + 2) = 0
👉
(x + 2)(x + 3) = 0
🔹
x = -2, -3 ✔
👉
4. Quadratic Formula
Formula:
🔹
x = (-b ± √(b² - 4ac)) / 2a
👉
5. Discriminant (D)
👉
D = b² - 4ac
If:
D > 0 → 2 real solutions
D = 0 → 1 solution
🔹
D < 0 → no real solution
👉
6. Solving by Formula
Example:
x² + 4x + 4 = 0
a = 1, b = 4, c = 4
👉
D = 16 - 16 = 0
🔹
x = -2 ✔
👉
7. Word Problem
A number multiplied by itself and added to 5 times gives 6
Equation:
🔹
x² + 5x - 6 = 0
8. Practice Questions
x² + 7x + 10 = 0
x² - 9 = 0
✅
x² + 6x + 9 = 0
Answers:
x = -5, -2
x = 3, -3
🔹 1. What is a Quadratic Equation?
👉 Standard form:
A quadratic equation is an equation of degree 2.
👉 Example:
ax² + bx + c = 0
🔹 2. Types of Quadratic Equations
x² + 5x + 6 = 0
Complete → x² + 5x + 6 = 0
🔹
Incomplete → x² – 9 = 0
👉
3. Factorization Method
Example:
👉
x² + 5x + 6 = 0
👉
Factors of 6 = 2, 3
👉
x² + 2x + 3x + 6 = 0
👉
x(x + 2) + 3(x + 2) = 0
👉
(x + 2)(x + 3) = 0
🔹
x = -2, -3 ✔
👉
4. Quadratic Formula
Formula:
🔹
x = (-b ± √(b² - 4ac)) / 2a
👉
5. Discriminant (D)
👉
D = b² - 4ac
If:
D > 0 → 2 real solutions
D = 0 → 1 solution
🔹
D < 0 → no real solution
👉
6. Solving by Formula
Example:
x² + 4x + 4 = 0
a = 1, b = 4, c = 4
👉
D = 16 - 16 = 0
🔹
x = -2 ✔
👉
7. Word Problem
A number multiplied by itself and added to 5 times gives 6
Equation:
🔹
x² + 5x - 6 = 0
8. Practice Questions
x² + 7x + 10 = 0
x² - 9 = 0
✅
x² + 6x + 9 = 0
Answers:
x = -5, -2
x = 3, -3
