📘 Today’s Maths Topic: Quadratic Equations (Basics & Easy Method with examples )

✨ What is a Quadratic Equation?

A quadratic equation is an equation where the highest power of the variable is 2.

👉 Standard form:

$ax^2 + bx + c = 0$

Where:

• a, b, c are numbers
• a ≠ 0

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📌 Example:

$$x^2 + 5x + 6 = 0$$

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🔍 Method 1: Factorization (Easy Method)

Step 1: Find two numbers

• Multiply = 6
• Add = 5

👉 Numbers are 2 and 3

Step 2:$$x^2 + 2x + 3x + 6 = 0$$

Step 3:$$x(x+2) + 3(x+2) = 0$$

Step 4:$$(x+2)(x+3) = 0$$

👉 Final Answer:$$x = -2,\quad x = -3$$

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🎯 Real-Life Example:

If you throw a ball upward, its height follows a quadratic equation 📈

🔍 Method 2: Quadratic Formula

Use when factorization is difficult 👇

$x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$

Example:

$$x^2 + 4x + 1 = 0$$

👉 Here:

• a = 1, b = 4, c = 1

$$x = \frac{-4 \pm \sqrt{16 – 4}}{2}$$

👉 Final Answer:$$x = -2 \pm \sqrt{3}$$

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📊 Discriminant (Important Concept)

$D = b^2 – 4ac$

👉 Based on D value:

• D > 0 → Two real solutions
• D = 0 → One solution
• D < 0 → No real solution

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🎯 Real-Life Example:

• Height of a ball 📈
• Profit & loss problems
• Area calculations

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🧠 Practice Questions:

$x^2 + 2x + 5 = 0$

$x^2 + 7x + 10 = 0$

$x^2 – 5x + 6 = 0$

Learn quadratic equations in a simple way with step-by-step examples. Perfect for students and beginners.