Discriminant Δ and Solution Set Types
Discriminant Δ = b² - 4ac. - Δ > 0: The equation has two distinct real roots x₁, x₂. - Δ = 0: The equation has one (repeated) real root x₀. - Δ < 0: The equati…
Syllabus path: Sets and Inequalities › Basic Properties and Solutions of Inequalities › Quadratic Inequalities
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CSCA Mathematics Formula Reference
Formula and explanation
Discriminant Δ = b² - 4ac. - Δ > 0: The equation has two distinct real roots x₁, x₂. - Δ = 0: The equation has one (repeated) real root x₀. - Δ < 0: The equation has no real roots. Explanation: The value of the discriminant directly affects the graph of the corresponding quadratic function (its intersection with the x - axis), thereby determining the solution set of the inequality.
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Quadratic Inequalities
Quadratic Inequalities Quadratic inequalities are a high - frequency topic in the CSCA exam. The core strategy is "Combining Algebra and Geometry"—using the graph (parabola) of the quadratic function y = ax²⁺bx + c to determine the range of x. 1. Standard Solution Steps Mnemonic:…
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