Solution Set Mnemonic for Quadratic Inequalities ( a > 0, Δ > 0 )
Let x₁, x₂ ( x₁ < x₂ ) be the two roots of ax²⁺bx + c = 0. - Solution set for ax²⁺bx + c > 0: x < x₁ or x > x₂. - Solution set for ax²⁺bx + c < 0: x₁ < 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
Let x₁, x₂ ( x₁ < x₂ ) be the two roots of ax²⁺bx + c = 0. - Solution set for ax²⁺bx + c > 0: x < x₁ or x > x₂. - Solution set for ax²⁺bx + c < 0: x₁ < x < x₂. Explanation: When the leading coefficient a > 0, the parabola opens upward. This mnemonic ("greater than takes the outside, less than takes the between") applies when the discriminant is greater than zero.
Related tutorial and examples
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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