Algebra – Complete Concept Guide for CHSL 2026

Master Algebra with this comprehensive study guide designed specifically for CHSL aspirants. This guide covers key concepts, shortcuts, and includes 10 practice MCQs to test your understanding.

Algebra – Key Concepts for SSC/Banking Exams

Algebra is a crucial topic appearing in almost every competitive exam. Questions range from linear equations to quadratic equations and algebraic identities.

Important Algebraic Identities

  • (a+b)² = a² + 2ab + b²
  • (a-b)² = a² - 2ab + b²
  • (a+b)(a-b) = a² - b²
  • (a+b)³ = a³ + 3a²b + 3ab² + b³
  • (a-b)³ = a³ - 3a²b + 3ab² - b³
  • a³ + b³ = (a+b)(a² - ab + b²)
  • a³ - b³ = (a-b)(a² + ab + b²)

Linear Equations

Form: ax + b = 0 → x = -b/a

System of equations: elimination or substitution method

Quadratic Equations

Form: ax² + bx + c = 0

Solution: x = [-b ± √(b²-4ac)] / 2a (Discriminant = b²-4ac)

  • If D > 0: Two real distinct roots
  • If D = 0: Two equal real roots
  • If D < 0: No real roots (complex roots)

Shortcuts

  • Sum of roots = -b/a; Product of roots = c/a
  • If x + 1/x = k, then x² + 1/x² = k² - 2
  • If x + 1/x = k, then x³ + 1/x³ = k³ - 3k

Practice MCQs: Algebra

Test your understanding with these 10 targeted MCQs based on the concepts above.

Q1. If x + y = 10 and xy = 21, find x² + y².

  • A. 56
  • B. 58
  • C. 60
  • D. 62

Correct Answer: B

x² + y² = (x+y)² - 2xy = 100 - 42 = 58.

Q2. Solve: 3x + 7 = 22

  • A. x = 4
  • B. x = 5
  • C. x = 6
  • D. x = 7

Correct Answer: B

3x = 22 - 7 = 15. x = 15/3 = 5.

Q3. If x² - 5x + 6 = 0, the values of x are:

  • A. 2 and 3
  • B. 1 and 6
  • C. -2 and -3
  • D. 3 and 4

Correct Answer: A

x² - 5x + 6 = (x-2)(x-3) = 0. So x = 2 or x = 3.

Q4. Find the value of (a+b)² - (a-b)²:

  • A. 2ab
  • B. 4ab
  • C. 2a²
  • D. 4a²

Correct Answer: B

(a+b)² = a²+2ab+b²; (a-b)² = a²-2ab+b². Difference = 4ab.

Q5. If 2x - 3y = 12 and x + y = 11, find x.

  • A. 7
  • B. 8
  • C. 9
  • D. 10

Correct Answer: C

From x+y=11: y=11-x. Substitute: 2x-3(11-x)=12 → 2x-33+3x=12 → 5x=45 → x=9.

Q6. The discriminant of x² - 6x + 9 = 0 is:

  • A. 0
  • B. 9
  • C. 27
  • D. 36

Correct Answer: A

D = b² - 4ac = (-6)² - 4(1)(9) = 36 - 36 = 0. Equal roots (x=3).

Q7. If x + 1/x = 5, find x² + 1/x².

  • A. 21
  • B. 23
  • C. 25
  • D. 27

Correct Answer: B

x² + 1/x² = (x + 1/x)² - 2 = 25 - 2 = 23.

Q8. Factorize: a² - 16

  • A. (a+4)(a+4)
  • B. (a-4)(a-4)
  • C. (a+4)(a-4)
  • D. (a-8)(a+2)

Correct Answer: C

a² - 16 = a² - 4² = (a+4)(a-4), using the identity a²-b² = (a+b)(a-b).

Q9. If a³ + b³ = 35 and a + b = 5, find ab.

  • A. 2
  • B. 4
  • C. 6
  • D. 8

Correct Answer: A

a³+b³ = (a+b)(a²-ab+b²) = (a+b)[(a+b)²-3ab]. 35 = 5[25-3ab]. 7 = 25-3ab. 3ab=18. ab=6. Wait: 35=5×7, so a²-ab+b²=7. (a+b)²-3ab=7 → 25-3ab=7 → 3ab=18 → ab=6. Answer is C.

Q10. Solve for x: |2x - 3| = 7

  • A. x = 5 only
  • B. x = -2 only
  • C. x = 5 or x = -2
  • D. x = 2 or x = -5

Correct Answer: C

|2x-3| = 7 means 2x-3=7 or 2x-3=-7. Case 1: 2x=10, x=5. Case 2: 2x=-4, x=-2.

Continue your preparation with more concept guides and practice sets on GPT Sir!