Discriminant and Nature of Roots

The discriminant is Δ = b² - 4ac. - If Δ > 0, the equation has two distinct real roots. - If Δ = 0, the equation has one repeated real root (a double root). -…

Syllabus path: Sets and Inequalities › Basic Properties and Solutions of Inequalities › Quadratic Inequalities

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CSCA Mathematics Formula Reference

Formula and explanation

The discriminant is Δ = b² - 4ac. - If Δ > 0, the equation has two distinct real roots. - If Δ = 0, the equation has one repeated real root (a double root). - If Δ < 0, the equation has no real roots. Applicable Condition: Quadratic equation ax² + bx + c = 0 ( a eq 0 ). Explanation: The sign of the discriminant directly affects how the graph of the quadratic function intersects the x - axis, which in turn determines the form of the solution set for the corresponding 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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