Question

5. Determine the real root of of f (x) = 3x - 4x2 +5x-3 ** using the bisection method. Employ initial guesses of x= 0 and Xu = 1 and iterate until the relative error Ea S 30%. Solution Step 1: x=0.5; f(x) = -1.125; Step 2: x = 0.75; f(x) = -0.2344; and &= 33.3% Step 3.x=0.875; f(x) = 0.322; and Ex = 14.2857%

a step by step walkthrough of your methods would be appreciated

*since the provided answer is wrong can you instead solve for the correct one?*

Answer 1

het see first the bisection method before solving the problem het fcx) be the given equation 1 Find two points 'a' and 'b' such that a<b. fca)x f(b) zo 2. Find the midpoint of a and het t = atb 3. If it is a soot then f(t) = 0 if not find f(t) f (6) Love take bat. azt otherwise then take 4. Repeat the steps until f (t) = 0 above f(t) = 0 but not exactly Note equal for approximate root to zero points as 3 . Here ton) - 3x² - 4x² + 5x-3. x =0 and xu=1 I'm here renaming intial and final a and b ie a=0 and b=1 We want relative erroe Ea - 30% relative error = knew - old x 1000 n new

Leto have a in form b It of table. fca) f(x) = 323 - 4 2² + 5x 3. 706 & (+) Iterations Ea=itita 0. 5 3x09 - 4X0²+ sxo-3 3x13_4X13+5x1-3 3x0.53_ 4x0.53 5x0.5-3=-1.125. = -3 0.75 -1.125 3x0.753 - 4x0.15² 0.45-0.5 100 5x0.75-3- 0.75 -0.2354 = 33.33% |3x0.818² - 4x0.875 0.875-0.75 000 + 5x0.875-3 0.975 = 0.3226 T= 14.2857% 0.875 -0.2344 3 0-75 iterations |-1.125x1 <0 a= o.s. CON 2 -0-2344x1 < a= 0.75 29.26X1 > b=0.875 → for rent iteahon-