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Quadratic inequalities

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Useful for: IB Math AA SL & HL AP® Precalculus

Learn it Solve ax² + bx + c > 0 (or < 0) by finding the roots, sketching the parabola, and reading where it is above (or below) the x-axis. For a > 0: '< 0' is between the roots; '> 0' is outside them.

Example: Solve x² − x − 6 < 0.

  1. Roots: (x − 3)(x + 2) = 0 → x = −2, 3.
  2. The parabola opens up, so it is negative between the roots: −2 < x < 3.

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