Bisection method is used for finding root of the function in given interval.

### Algorithm:

```IN:
Function f, which is continous function and interval [a,b]. Function must satisfy given equation: f(a) * f(b) < 0 - signs of that values are different, which means that given function in given interval has at least one root in interval [a,b].
OUT:
Root in given interval.
1. Calculate c - midpoint of given interval using formula: c = (a + b) / 2.
2. Calculate f(c).
3. If b - a is small enough or abs(f(c)) is small enough: return c - which is the root we were searching for;
4. If(f(a) * f(c) < 0) assign c to b, else assign c to a.
5. Go to step 1.```

### Step By Step:

• Bisection Method Step 1

### Sample Output:

```f(x) = x * (x * (x * (x * (x)) + 2)) - 2
[0,2]

root: 0.8515625```

## Bisection Method Step By Step

Iteration Numberacbf(cn)
10121
200.51-1.4375
30.50.751-0.55859375
40.750.87510.117431640625
50.750.81250.875-0.2438812255859375
60.81250.843750.875-0.0693502426147461
70.843750.8593750.875 0.022470533847808838
80.843750.85156250.859375 -0.023827489465475082

### Pros:

• easy to implement.
• no need to calculate derivative of given function.

### Cons:

• slow compared to other methods.

Bisection Method Algorithm
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