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Consider the function ?(?) = ?^2 − 3? − 2. a) Use Newton’s Method to estimate...

Consider the function ?(?) = ?^2 − 3? − 2.
a) Use Newton’s Method to estimate a root for the function given by the above formula. More precisely: Using the initial value of ?1 = 5, calculate ?3.

b) Solve the quadratic equation ?^2 − 3?− 2 = 0 and compute the two solutions to 4 decimal places. How do these compare to the approximate root you computed in part (a) above?

c) Suppose your friend uses Newton’s Method to estimate a root for the equation ?^2 − 3? − 2 = 0 using the initial value of ?1 = −3. Using a graph of the function ?(?), explain why your friend is likely approximating a different number than you did in part (a).

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