Bisection method
General · Mathematics
Study notes
Q: Use bisection to approximate √2 (root of x²-2) starting [1,2], 3 steps. f(1) = -1, f(2) = 2: sign change ✓. Step 1: c = 1.5: f = 0.25 > 0: [1,1.5]. Step 2: c = 1.25: f = -0.4375 < 0: [1.25,1.5]. Step 3: c = 1.375: f = -0.109 < 0: [1.375,1.5]. √2 ≈ 1.4375 ± 0.0625! (Slow but sure!)