Chapter 2 – Quadratic Equations and Inequalities

This section demonstrates how to solve systems of linear equations and quadratic equations graphically. You'll learn to find points of intersection by plotting graphs and identifying where they cross the x-axis.

This section teaches you how to form a quadratic equation when its roots are given, using the formula \(x^2 - Sx + P = 0\), where \(S\) is the sum of roots and \(P\) is the product of roots.

This section covers the discriminant \(b^2 - 4ac\) and how it determines the nature of roots. You'll learn to identify whether roots are real and equal, real and unequal, rational, irrational, or imaginary.

This section introduces quadratic inequalities and teaches you how to solve them using the critical points method. You'll learn to identify intervals where the inequality holds true.

This section covers rearranging formulas to make a different variable the subject. You'll learn to apply algebraic operations to isolate a specific variable in various scientific and mathematical formulas.

This section applies quadratic equations to real-world problems including population models, profit maximization, projectile motion, and economic optimization. You'll learn to model and solve practical scenarios.

The review exercise mixes questions from all sections of Chapter 2, giving you a chance to test your understanding across topics including MCQs, solving quadratic equations by factorization, completing square, quadratic formula, nature of roots, and real-world applications.