Solve inequalities of the form ax² + bx + c [SIGN] 0 and visualize the solution intervals.
Input Parameters
Solution Intervals
(-∞, 2.00) ∪ (3.00, ∞)
Solution Set
The set of all x-values that satisfy the inequality.
Solution Steps:
•Identify coefficients: a=1, b=-5, c=6
•Parabola opens Upward (a > 0)
•Solve the equality ax² + bx + c = 0 to find critical points.
•Test intervals and select region satisfying "> 0".
About this calculator
Solving Quadratic Inequalities
Solving a quadratic inequality involves finding the intervals on the x-axis where the parabola is either above or below zero. The key steps are finding the critical points (roots of the related equation) and testing the intervals between these points using a sign chart or the parabola's concavity.
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Pro Tips
Find Roots First: Solve ax² + bx + c = 0 to find the boundaries of your intervals.
Check Concavity: If a > 0 (opens up) and you want > 0, the solution is 'outside' the roots. If you want < 0, it's 'between' the roots.
Inclusion: Use square brackets [ ] for ≤ and ≥, and parentheses ( ) for < and >.
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Fun Facts
"Inequalities are used extensively in optimization problems where resources are limited (e.g., spending ≤ budget)."
"Thomas Harriot (1560-1621) was the mathematician who introduced the > and < symbols."
