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1. What is a Quadratic Equation?
• A quadratic equation has the form: ax² + bx + c
= 0
• - a, b, and c are numbers
• - x is the unknown variable.

2. What are Roots?
• Roots are the solutions of a quadratic
equation.
• They are the values of x that make the
equation equal to 0.

3. Example of Roots
• Example:
• Solve x² - 5x + 6 = 0
• Roots are x = 2 and x = 3.

4. What is the Discriminant?
• Discriminant (D) tells the type of roots.
• Formula: D = b² - 4ac

5. Types of Roots Based on
Discriminant
• If D > 0: Two different real roots
• If D = 0: Two equal real roots
• If D < 0: Two complex roots

6. Sum of the Roots
• Sum of roots = -b/a
• (Negative of b divided by a)

7. Example for Sum of Roots
• For 2x² - 4x + 1 = 0:
• Sum = -(-4)/2 = 2

8. Product of the Roots
• Product of roots = c/a
• (Constant term divided by a)

9. Example for Product of Roots
• For 2x² - 4x + 1 = 0:
• Product = 1/2

10. Relationship Summary
• Sum of roots: -b/a
• Product of roots: c/a
• Discriminant: b² - 4ac
• These connect roots with coefficients.

11. Importance of These Relationships
• Helps in solving equations faster.
• Helps to know graph behavior.
• No need to fully solve sometimes.

12. Final Example
• Given x² - 3x + 2 = 0:
• Sum = 3
• Product = 2
• Discriminant = 1 (two real roots)