Nature of Roots
Gr 11

The Grade 11 Nature of Roots module helps learners analyse quadratic equations by examining the discriminant and understanding what it reveals about the solutions of the equation. This chapter strengthens algebraic reasoning and prepares students for more advanced quadratic work in Grade 12.

Learners explore the standard form of a quadratic equation, ax2+bx+c=0ax^{2} + bx + c = 0ax2+bx+c=0, and use the discriminant Δ=b2−4ac\Delta = b^{2} - 4acΔ=b2−4ac to determine whether the equation has two real solutions, one real solution, or no real solutions. Lessons also cover the connection between the discriminant and the graph of a parabola—helping students interpret how the number of roots relates to the parabola’s intersection with the x-axis. Step-by-step examples guide learners through calculating the discriminant, classifying roots, and applying this knowledge in problem-solving contexts.

By the end of this module, students will be able to determine the nature of roots accurately, interpret quadratic equations graphically and algebraically, and apply discriminant analysis confidently—forming an essential foundation for more advanced algebra and calculus in the senior grades.