SSC CHSL · Bite-size lessons

Algebra

About 6 min · Quantitative Aptitude (Basic Arithmetic Skill) · English

Time worked out from the lesson's 337 words at 150 words a minute, plus a minute for each question.

The exam focuses on three pillars: solving linear and quadratic equations, applying polynomial identities, and factorising expressions. Mastery here is non-negotiable because algebra underpins several other topics like time-speed-distance word problems and profit-loss equations.

Key ideas

• Linear equation in one variable: An equation of the form ax + b = 0 where a ≠ 0. Solution is x = –b/a. Always isolate the variable on one side by performing inverse operations.
• Linear equation in two variables: Form ax + by = c. SSC CHSL typically gives simultaneous equations (a pair) which you solve by substitution, elimination, or cross-multiplication to find unique values of x and y.
• Quadratic equation: Standard form ax² + bx + c = 0 where a ≠ 0. Solutions come from factorisation, completing the square, or the quadratic formula x = (–b ± √(b² – 4ac)) / 2a.
• Discriminant (D): For ax² + bx + c = 0, D = b² – 4ac. If D > 0, two distinct real roots; D = 0, two equal real roots; D < 0, no real roots (complex roots).
• Polynomial identities: Pre-memorised algebraic formulas that let you expand or factorise expressions in one step. SSC CHSL tests the ability to recognise which identity fits a given expression.

Quick reference

• Linear one variable: ax + b = 0 → x = –b/a
• Quadratic formula: x = (–b ± √(b² – 4ac)) / 2a
• (a + b)² = a² + 2ab + b²; (a – b)² = a² – 2ab + b²
• a² – b² = (a + b)(a – b)
• a³ + b³ = (a + b)(a² – ab + b²); a³ – b³ = (a – b)(a² + ab + b²)

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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