Class 10 Quadratic Equations Cheat Sheet

Key Definitions

• Quadratic Equation: An equation of the form ax² + bx + c = 0, where a ≠ 0.

• Roots: Solutions of the quadratic equation, can be real or complex.

• Discriminant (D): Given by D = b² - 4ac, determines the nature of roots.

Important Formulas

• Quadratic Formula:

  x = (-b ± √D) / (2a)
  

• x: Roots of the equation

• a: Coefficient of x²

• b: Coefficient of x

• c: Constant term

• D: Discriminant

Critical Concepts

• Nature of Roots:

• If D > 0: Two distinct real roots

• If D = 0: One real root (repeated)

• If D < 0: Two complex roots

• Factoring:

• Factor ax² + bx + c into (px + q)(rx + s).

• Vertex Form:

• y = a(x - h)² + k, where (h, k) is the vertex.

Common Mistakes to Avoid

• Forgetting to check if a = 0 (not a quadratic).

• Miscalculating the discriminant.

• Mixing up signs while applying the quadratic formula.

Quick Memory Tricks

• Discriminant Determines roots:

• D > 0: Distinct

• D = 0: Duplicate

• D < 0: Complex

• "Factor": Remember "FOIL" (First, Outside, Inside, Last) for multiplying binomials.

Key Diagrams

• Parabola Shape:

      |
      |         *
      |           
      |             
      |               
      |____________________
  

• Represents the graph of a quadratic function, opening upwards if a > 0 and downwards if a < 0.

• Axis of Symmetry:

• Vertical line x = -b/(2a) divides the parabola into two symmetrical halves.

Tip: Always check for factorization before using the quadratic formula; it can save time!

Practice: Solve at least 5 different types of quadratic equations to familiarize with various methods.