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In this programming exercise we will use PYTHON to implement the root finding algorithms taught in class. Write a PYTHON program to implement the false

In this programming exercise we will use PYTHON to implement the root finding algorithms taught in class.
Write a PYTHON program to implement the false position method to find the roots of equation
f(x)=2xcos(2x)-(x-2)2,
accurate up to four significant digits.
a) First, define a PYTHON function in the following manner:
def falsepos(func, a, b, es):
where func represents f(x),a,b the bracket and es is the stopping criteria. Thereafter, call this function
for different brackets to find the roots. Report their values.
b) Make a plot of f(x) vs.x and identify these roots via markers.
c) Verify your solutions using the in-built PYTHON function brentq for Brent's method. Note that you need
to import scipy to access this function.
Now write a PYTHON function to implement the secant method:
def falsepos(func,x0, x1, es):
where x0,x1 are the two starting points.
a) Use the function to find roots of f(x)=x4+65x3+86x+128, accurate up to 4 significant digits. Report
their values.
b) Again make a plot of the above function to and mark all the roots.
c) Verify your solutions using the in-built PYTHON function roots, which is available in numpy.
Utilizing the above functions, find the shortest distance between the curve y=x2+1 and the point (1,0).
Report the shortest distance. Which method converges faster, the false position or the secant method? (report
the number of iterations in both cases).
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