a$)$ Find the positive real root of $f(x)=x^4-8x^3-35x^2+450x-1001$ using the falseposition method. Use initial guesses of $x_1=4\mathrm{.}5$ and $x_u=6$ and performs five iterations. Compute both the true and approximate errors based on the fact that the root is $5\mathrm{.}60979.$ Use a plot to explain your results and perform the computation to within ${}_s=1\mathrm{.}0\%.$

b$)$ Write pseudo code for computing ${}_s.$