Exercise 2.5 Class 10 Math Solutions – Unit 2 Quadratic Equations and Inequalities, Punjab Board
Step-by-step solutions to Exercise 2.5 of Unit 2: Quadratic Equations and Inequalities for Class 10 Punjab Board students. Covers solving quadratic inequalities in one unknown (ax² + bx + c > 0, < 0, ≥ 0, ≤ 0) using critical values, test intervals, and number line solution sets.
Exercise Overview
Exercise 2.5 introduces quadratic inequalities in one unknown within Unit 2: Quadratic Equations and Inequalities for Class 10 Punjab Board students. Moving beyond exact equation equality, students explore inequalities of the form ax² + bx + c > 0, ax² + bx + c < 0, ax² + bx + c ≥ 0, and ax² + bx + c ≤ 0. The objective is to discover all continuous intervals of real numbers that satisfy the inequality condition.
The standard method taught in this exercise involves three systematic steps. First, students establish the associated quadratic equation ax² + bx + c = 0 to calculate the critical values (boundary roots). Second, these critical points divide the continuous real number line into distinct sub-intervals. Third, students test arbitrary sample values from each interval or analyze the signs of linear factors (x - r₁)(x - r₂) to determine which intervals satisfy the inequality, correctly presenting the final result in set-builder notation {x | x < r₁ or x > r₂} or bounded intervals.
In Punjab Board examinations (including Lahore, Rawalpindi, Gujranwala, Faisalabad, and Multan Boards), questions from Exercise 2.5 regularly test both algebraic factoring and logical inequality interpretation. Mastering interval tests and avoiding common strict versus non-strict inequality errors is essential. These step-by-step solutions provide the clear guidance needed to secure top marks in board exams.