We want to use Newton's method to approximate a root of the polyomial 9(93) : m5 7 8m4 7 53:2 + 13. (a) (2 points) On paper: 0 Use the Intermediate Value Theorem in an appropriate way to prove that a root exists, and 0 give an interval that contains a root. 0 Be sure to verify that all conditions to use the Intermediate Value Theorem are met. (b) (1 point) On paper: Write down the iterative formula of Newton's method in this case. (c) (1 point Mobius) Now apply Newton's method with the initial approximation $0 : 1, computing 2 iterations. Enter the approximate root 3:2 that you get below, with an accuracy of at least 4 decimal places. 9:2 : (to 4 decimal places)