Chapter 4 — Quadratic Equations

NCERT Class 10 Maths Chapter 4, Quadratic Equations, covers equations of the form ax² + bx + c = 0 (a ≠ 0) and teaches three methods to find their roots: factorisation, completing the square (leading to the quadratic formula), and the discriminant to determine the nature of roots.

Chapter 4 of NCERT Class 10 Mathematics introduces quadratic equations in standard form ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0. Students learn that a quadratic equation can have at most two roots, which are the same as the zeroes of the corresponding quadratic polynomial. The chapter covers solving equations by factorisation, and derives the quadratic formula x = (−b ± √(b²−4ac)) / 2a. The discriminant b²−4ac determines the nature of roots: two distinct real roots when positive, two equal real roots when zero, and no real roots when negative. Historical contributions from Brahmagupta, Sridharacharya, and Al-Khwarizmi are also noted.

1. 01A quadratic equation in standard form is ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0.
2. 02A quadratic equation has at most two roots; its roots are the same as the zeroes of the quadratic polynomial ax² + bx + c.
3. 03Roots can be found by factorisation: split the middle term, express as a product of two linear factors, and set each factor to zero.
4. 04The quadratic formula gives roots as x = (−b ± √(b²−4ac)) / 2a, valid when b²−4ac ≥ 0.
5. 05The discriminant (b²−4ac) determines the nature of roots: >0 means two distinct real roots, =0 means two equal real roots, <0 means no real roots.
6. 06Quadratic equations model many real-life situations such as dimensions of halls, speed of trains, and product of consecutive integers.