Q2. (Root finding) Solve the following equations by python codes. 1. Consider the nonlinear equation: 24 + 7x3 + 2x ++1=0. Firstly, plot the functions fi(x)= x4 + 723 + 2x2 + x +1 and f2(x) = 0 by matplotlib. The suggested range for x is from 7 to 2. From the plot, find the approximate roots. Secondly, try different initial guesses and find all the roots to the equation by scipy.optimize.root(). You can check the solutions with the approximate roots observed from the plot. 2. Consider the nonlinear equation: 1 sin Firstly, plot the functions fi(x) = sin x and f2(x) = 1/x by matplotlib. The suggested range for z is from 0.1 to 20. From the plot, find the approximate roots. Secondly, try different initial guesses and find all the roots to equation in the range ze [0.1, 20) by scipy.optimize.root(). You can check the solutions with the approximate roots observed from the plot 3. Consider the system of nonlinear equations: ry = 10 22 + y2 = 36 Firstly, plot the two functions by matplotlib. The suggested range is 2 (-7, 7), y (-7, 7). From the plot, find the approximate roots. Secondly, try different initial guesses and find all the roots to the equation by scipy.optimize.root(). You can check the solutions with the approximate roots observed from the plot. (10 + 10 + 10 marks)