Lesson 4.1: Algebra (Equations, Inequalities, Polynomials)

Algebra is a key part of the Mathematics section for NDA, CDS, and AFCAT exams. It helps aspirants solve problems related to equations, inequalities, and polynomials, which are frequently tested in competitive exams.

1. Equations

• Linear Equations: Equations of the form ax + b = 0

  • Example: Solve 2x + 5 = 11 → x = 3

• Quadratic Equations: Equations of the form ax² + bx + c = 0

  • Solutions using factorization, formula: x = [-b ± √(b²-4ac)] / 2a

• Simultaneous Equations: Two or more equations solved together

  • Substitution and elimination methods

2. Inequalities

• Linear Inequalities: ax + b > 0 or ax + b < 0

• Rules of Inequalities:

  • Adding/subtracting same number preserves inequality

  • Multiplying/dividing by negative number reverses inequality

• Graphical Representation: Solutions can be represented on a number line

3. Polynomials

• Definition: Algebraic expressions with variables and coefficients

  • Example: P(x) = 2x³ + 3x² – x + 5

• Types: Linear, Quadratic, Cubic, Higher-order

• Operations: Addition, subtraction, multiplication, division

• Factor Theorem: If P(a) = 0, then (x-a) is a factor of P(x)

• Remainder Theorem: Remainder when P(x) is divided by (x-a) is P(a)

Exam Tips

• Memorize basic formulas for equations, inequalities, and polynomials.

• Practice previous year NDA, CDS algebra questions.

• Focus on factorization, substitution, and simplification techniques.

• Solve at least 20–25 algebra problems daily for speed and accuracy.