A fast, one-glance recap of Class 10 Maths Chapter 4 (Quadratic Equations) — for the full worked explanations, see the Solutions.
Revision Notes: Quadratic Equations
- Standard form: ax²+bx+c = 0, where a≠0
- Roots: values of x that satisfy the equation; a quadratic equation has at most 2 roots
- Factorisation method: split the middle term so the equation becomes a product of two linear factors, then set each factor to zero
- Discriminant: D = b²−4ac
- D > 0 → two distinct real roots
- D = 0 → two equal (repeated) real roots
- D < 0 → no real roots
- Quadratic formula: x = [−b±√(b²−4ac)]/2a
- Sum of roots = −b/a, Product of roots = c/a
- Word problems: define the variable clearly, form the quadratic equation from the given condition, solve, then reject any root that doesn’t fit the real-world context (negative length, negative speed, non-integer count, etc.)
- Reciprocal-root trick: if one root is the reciprocal of the other, their product = 1, so c/a = 1, i.e. a = c
- Know by heart: the D>0 / D=0 / D<0 classification is a near-guaranteed 1–2 mark question every year
See also: Extra Questions (HOTS) | Formulas Handbook
