number itself should be included in your submission.
1. Determine the real root of f(x) = x5 − 10x4 + 46x3 − 90x2 + 85x − 31
(a) Graphically.
(b) Using the bisection method to determine the root with εs = 10%. Employ the initial guesses of xl = 0.5 and xu = 1.0.
(c) Perform the same computation as in (b) but use the false position methodand εs = 0.2%.
2. Determine the lowest real root of f(x) = −3x3 + 20x2 − 20x − 12
(a) Graphically.
(b) Using the bisection method to determine the lowest root with εs = 2%. Employ the initial guesses of xl = −1 and xu = 0.
(c) Perform the same computation as in (b) but using the false position method.
3. Textbook problem 5.13.
4. Determine the real roots of f(x) = 0.5x3 − 4x2 + 8x − 1
(a) Graphically.
(b) Using the Newton-Raphson method to within εs = 0.01%.
5. Determine all roots of f(x) = −3x3 + 20x2 − 20x − 12
(a) Using the Secant method to a value of εs corresponding to three significant figures.
