Algebra
Algebra
Algebra spans linear and quadratic equations, standard identities, the remainder theorem, and inequality rules. SSC CGL and banking papers dedicate 3\u20135 questions to this topic. Master the sum/product-of-roots shortcut and identity recognition to solve most questions without full expansion.
Key Idea
Convert word problems into equations, then solve. For quadratics, use the discriminant (b²−4ac) to determine the nature of roots without fully solving.
Core Formulas
Linear Equation (Two Variables) — Substitution / Elimination
ax + b = 0 → x = −b/a | For two variables: solve one equation for x, substitute into the other
Solve single-variable equations by direct substitution. For two variables, match coefficients for elimination or isolate one variable for substitution.
Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a | Sum of roots = −b/a | Product of roots = c/a
Find roots of ax\u00B2+bx+c=0. Apply sum/product shortcuts to answer root-relationship questions without computing each root separately.
Key Algebraic Identities
(a+b)² = a²+2ab+b² | (a−b)² = a²−2ab+b² | (a+b)(a−b) = a²−b² | a³+b³ = (a+b)(a²−ab+b²)
Simplify expressions or find missing values when two of the three terms are known; recognise the pattern first.
Remainder Theorem
Remainder when f(x) is divided by (x−a) = f(a) | If f(a)=0, (x−a) is a factor
Find remainder without performing polynomial long division; also used to check whether a given binomial is a factor.
Inequalities — Sign Flip Rule
Multiplying or dividing both sides by a negative number flips the inequality sign | |x| < a ⟺ −a < x < a
Solving inequalities involving negative coefficients or absolute values; always check whether you are multiplying by a negative.
Relevant Exams
Algebra is a high-weight topic in SSC and banking exams — expect 3–5 questions per paper. Quadratic roots, identity shortcuts, and age/number word problems are the most frequently tested sub-types.