Chapter 4: Quadratic Equations
Understanding Quadratic Equations
A quadratic equation is an expression of the form ax²+bx+c=0, where a≠0. These equations appear in many real-life situations, like calculating dimensions or solving puzzles involving sums and products. The chapter begins by illustrating how quadratic equations emerge from word problems. It also explores historical contributions from Indian and Arab mathematicians, including methods like completing the square, which led to the development of the quadratic formula.
Solving Quadratic Equations
Quadratic equations can be solved using various methods:
- Factorisation – Expressing the quadratic as a product of two linear factors.
- Quadratic Formula – Using x= (−b± b²−4ac )2a for equations of the form ax²+bx+c=0.
- The discriminant (b²−4ac) determines the nature of roots:
- If positive: two distinct real roots.
- If zero: two equal real roots.
- If negative: no real roots.
Illustrative examples and exercises help develop fluency in selecting and applying the correct method.
Applications in Daily Life
Quadratic equations model various real-world problems involving geometry, motion, and age-based scenarios. Students learn how to translate situations into equations and solve them logically. Problems include calculating dimensions, ages, speeds, and areas. The chapter emphasizes interpreting solutions meaningfully—like ignoring negative values when quantities must be positive—while reinforcing algebraic reasoning and decision-making.