JEE Main typically asks 1-2 questions from quadratic equations annually. The distribution: 40% on root nature and parameter ranges, 25% on symmetric functions and Vieta's formulas, 20% on location of roots, 15% on equations reducible to quadratics.
Most common PYQ pattern: "Find the range of parameter k such that [root condition]." These require setting up and solving D >= 0, f(boundary) conditions, and vertex conditions simultaneously. The intersection of all conditions gives the answer.
Second common pattern: "If alpha, beta are roots of [equation], find [expression in alpha, beta]." The expression is always symmetric and computable via Vieta's formulas. Trap: the expression looks asymmetric but simplifies to a symmetric one.
Third pattern: "The number of real roots of [equation with radicals/absolute values/exponentials]." These test substitution skills and domain awareness. Common trap: counting extraneous roots introduced by squaring.
Numerical answer type questions often ask for + (use recurrence), the value of a parameter (use common root or discriminant = 0), or the number of solutions (use graphical or substitution methods).
Key traps to avoid: (1) When asked "for all real x, f(x) > 0," students forget to check a > 0 in addition to D < 0. (2) In "both roots positive" problems, students forget one of the three conditions (D, sum, product). (3) In modulus equations like |f(x)| = g(x), students solve without ensuring g(x) >= 0. (4) In log equations, students forget domain restrictions.