The correct option is B 0.75,0.875,0.8125
We have to find the second,third and fourth approximation of root of the
equation x3+x2−1=0 in the interval (0,1) using successive
Bisection method.
Iteration 1: k=0
c0=a0+b02=0+12=0.5
Since f(c0)f(a0)=f(0.5)f(0)>0
Therefore set a1=0.5,b1=b0
Iteration 2: k=1
c1=a1+b12=0.5+12=0.75
Since f(c1)f(a1)=f(0.75)f(0.5)>0
Therefore set a2=c1,b2=b1
Iteration 3: k=2
c2=a2+b22=0.75+12=0.875
Since f(c2)f(a2)=f(0.875)f(0.75)<0
Therefore set a3=a2,b3=c2
Iteration 4: k=3
c3=a3+b32=0.75+0.8752=0.8125
Thus the second,third and fourth approximations are 0.75,0.875,0.8125 respectively.