Quadratic Equations

Board: GSEB Class: 10

Chapter Overview

A quadratic equation in x is of the form ax² + bx + c = 0, where a != 0. Solving methods: factorization (splitting the middle term), completing the square, and the quadratic formula. The discriminant D = b² - 4ac determines the nature of roots: D > 0 (two real distinct roots), D = 0 (two equal real roots), D < 0 (no real roots). Word problems involving quadratic equations cover areas, time-speed-distance, and number problems.

Topics Covered

Standard Form
Factorization Method
Completing the Square
Quadratic Formula
Discriminant
Nature of Roots
Word Problems

Key Formulas

x = (-b +/- √b² - 4ac) / 2a

D = b² - 4ac

D > 0: real and distinct

D = 0: real and equal

D < 0: no real roots

Real-World Applications

Applications: Projectile motion, optimization problems, area calculations, engineering design.

Study Tips

Tip: Master the quadratic formula

Tip: Practice completing the square method

Tip: Check your answers by substitution