Step by Step Solver to Solve Quadratic Inequalities

Solve quadratic inequalities of the form \( ax^2 + bx + c > 0 \) (or \( \ge, <, \le \)) using discriminant analysis. Roots are shown in exact simplified form. Generate random practice problems with step-by-step solutions and graphical verification.

📐 Quadratic Inequality Solver

Solve \( ax^2 + bx + c \; \gt \; 0 \) (or ≥, <, ≤) — exact roots, interval notation

\( x^2 - 3x + 2 > 0 \)
Solve the inequality. Click "Show me" for each step.

📖 Step-by-Step Solution

STEP 1: Rewrite with 0 on the right side
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STEP 2: Find discriminant & apply rules
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STEP 3: Solution set in interval notation
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📊 Graph of \( y = ax^2 + bx + c \)
Blue curve: parabola | Red points: x-intercepts (roots)

The solution set corresponds to x-values where the parabola satisfies the inequality.