Question

Solve the equation x3 – 7 = 0 using the bisection algorithm starting with ap = 1 and bo = 2. Conduct three iterations and report the approximation of the root computed by the algorithm. Use as many digits as possible. Answer:

Answer 1

Given function fix)= x 37 90= 1 bar 2 feo) = 137= -6 (ave) fo)= I eve) 23 2 = 8-7= The frana Eign) + fog light + Root must lies bedween 902 qotto 142 3 = 15 7 fico)=lis 3.625 eve) fea] =Eve), and of Bo) = are) fico) = tve) fit) sign of ffre) eigh So Root lies between coabo 4.5+2 do= C + 2 = Fida)= 1.7537 =-1.64 five) 1 Ietenationa = 1.25 2 Iteratona @or 1.75f? fieb).foo) sijen = Fredx tve's reco So Root lees will be open les between doz bo door freo)= lisas? =-0.4 or are] syn freo)x Begen flba) s -ve co so Root colll lies between corso fo- *#* = 1.8491? 1.495 ? = 1.9375– 2 alifat Istent rays for conta

1.93753 7 to O 0.27 (tive) Now, trextre) =ovelo so rost colll lie between for fofco 1.s375f lifar sign fefox x Sigh fleo) = Iterationy. 2 = 1.90625 2 figo) 1. 906293 2 19 oio7 no Thus After three Iteration Root 13 Ro pot of Амеч e quattroy Is 1.90625 निय 1.9375