Find the the root root x ^ 3 - x ^ 2 + x - 7 = 0 of equcation Correct three Bisection using decimal method place
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Answer:
1.375
Step-by-step explanation:
We have to find the third approximation of root of the equation x
3
−x
2
−1=0 in the interval (1,2) using successive Bisection method.
Iteration 1: k=0
c
0
=
2
a
0
+b
0
=
2
1+2
=1.5
Since f(c
0
)f(a
0
)=f(1.5)f(1)<0
Therefore set a
1
=a
0
,b
1
=c
0
Iteration 2: k=1
c
1
=
2
a
1
+b
1
=
2
1+1.5
=1.25
Since f(c
1
)f(a
1
)=f(1.25)f(1)>0
Therefore set a
2
=c
1
,b
2
=b
1
Iteration 3: k=2
c
2
=
2
a
2
+b
2
=
2
1.25+1.5
=1.375
Thus the third approximation of the root is 1.375 respectively.
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