The famous Wilkinson polynomial is defined as $P(z)=pro{d}_j=1^{20}(z-j).$ Hence, its zeros are the integers from $1$ to $20.$ You can find

the coefficients for this polynomial in a blog post by Cleve Moler $($the inventor of Matlab$).$

The coefficient of $z^{20}$ of the exact Wilkinson polynomial is $1.$ Perturb this coefficient to be $1+lon,$ where $lon={10}^{-10}.$

$($a$)$ Using the roots command of Numpy, compute the corresponding zeros of the perturbed polynomial and plot them with

matplotlib. pyplot in the complex plane using blue crosses. Also, plot the exact zeros of the unperturbed Wilkinson polynomial

using red circles $($for both, use the corresponding options in the plot function of Matplotlib$).$ You want to draw the exact roots

first so that the crosses overlay the circles. Your answer should contain your plot in jpg or png image format.

$($b$)$ Interpret the perturbations you see in the plot. What magnitudes of condition numbers for the zeros would you expect from

your observation?