Class 10 Maths (Ganit) Chapter 4 PDF: द्विघात समीकरण (Quadratic Equations)

Class 10 Maths Chapter 4, Quadratic Equations, covers standard quadratic equations ax² + bx + c = 0 (a ≠ 0), solving them by factorisation and by the quadratic formula, and determining the nature of roots using the discriminant D = b² – 4ac.

What Class 10 Mathematics (Ganit — Hindi Medium) Chapter 4 Covers

4.1 & 4.2 Quadratic Equations & Solution by Factorisation formulates word problems as ax² + bx + c = 0 (a ≠ 0) and solves them by splitting the middle term into linear factors.

4.3 Nature of Roots & Quadratic Formula applies the quadratic formula x = -b ± √(b² – 4ac) / 2a and analyses the discriminant D = b² – 4ac: (1) two distinct real roots if b² – 4ac > 0; (2) two equal real roots ($-b/2a$) if b² – 4ac = 0; (3) no real roots if b² – 4ac < 0.

Exercises in Chapter 4

• Exercise 4.1 (2 Questions) checks whether given equations are quadratic and sets up quadratic equations from area, consecutive integer, age and train-speed situations.
• Exercise 4.2 (6 Questions) finds roots of quadratic equations by factorisation, including right-triangle altitude problems and cottage industry pottery cost problems.
• Exercise 4.3 (5 Questions) tests the nature of roots using b² – 4ac, finds k for two equal roots, and solves rectangular mango grove and park design problems.

Read Class 10 Mathematics (Ganit — Hindi Medium) Chapter 4 Online

More Chapters

• Previous: Chapter 3: दो चर वाले रैखिक समीकरण युग्म (Pair of Linear Equations in Two Variables)
• Next: Chapter 5: समांतर श्रेढ़ियाँ (Arithmetic Progressions)
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FAQ

What is the quadratic formula and the discriminant of ax² + bx + c = 0?
The roots of ax² + bx + c = 0 (a ≠ 0) are given by x = -b ± √(b² – 4ac) / 2a, where D = b² – 4ac is called the discriminant.

How does the discriminant D = b² – 4ac determine the nature of roots?
If $D > 0$, the quadratic equation has two distinct real roots; if $D = 0$, it has two equal real roots (each equal to $-b/2a$); if $D < 0$, it has no real roots.