Solution Set Rules for Quadratic Inequalities (a > 0)

For ax² + bx + c > 0 ( a > 0 ) with Δ > 0, let the roots of the equation be x₁, x₂ ( x₁ < x₂ ). - The solution set for ax² + bx + c > 0 is: x < x₁ or x > x₂. -…

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

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CSCA Mathematics Formula Reference

Formula and explanation

For ax² + bx + c > 0 ( a > 0 ) with Δ > 0, let the roots of the equation be x₁, x₂ ( x₁ < x₂ ). - The solution set for ax² + bx + c > 0 is: x < x₁ or x > x₂. - The solution set for ax² + bx + c < 0 is: x₁ < x < x₂. Applicable Condition: a > 0, discriminant Δ > 0. Explanation: When the leading coefficient is positive, the parabola opens upwards. For 'greater than 0', take the intervals outside the roots; for 'less than 0', take the interval between the roots. This is the core mnemonic for solving.

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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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