Back to revision notes Open full-size SVG Print mind map M20 Iteration and quadratic inequalities mind map Use your browser’s Print command for A4 landscape, or choose A3 in its paper settings. The SVG remains sharp when enlarged. A text version follows the map.
Read the mind map as text Iterate Feed back: Higher: xₙ₊₁ uses xₙ; choose rearrangement and starting x₀Sequence: Higher: x₀=1 in √(xₙ+2) → 1.7321,1.9319,1.9829…Convergence Behaviour: Higher: May converge or diverge; oscillations can do either; preserve precisionMissing root: Higher: Positive square-root scheme misses root −1Root bracket: Higher: Continuous sign change brackets root; trial refines intervalQuadratic intervals Roots first: Higher: Roots split number line; inspect signs between/aroundExample: Higher: x²−5x+6 < 0 → 2 < x < 3Check / endpoints Either interval: Higher: x²−5x+6 ≥ 0 → x ≤ 2 OR x ≥ 3Inclusion: Higher: ≤/≥ include roots; </> exclude; test each intervalNegative leading: Higher: Sign pattern reverses; 6−x−x² > 0 → −3 < x < 2Connections Iterate → Convergence: Rearrangement affects iteration convergence Quadratic intervals → Check / endpoints: Boundary roots divide an inequality into intervals 