Let f(x) x3 8x 5. (a) Use Descartess rule to explain in complete sentences why the

Chapter 12, Problem 23

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Let f(x) x3 8x 5. (a) Use Descartess rule to explain in complete sentences why the equation f(x) 0 has no positive roots and exactly one negative root. (If you need help, see Example 4 in the text.) (c(b) Use a graph to confirm the results in part (a). That is,graph y f(x) and note that there is but one x-interceptand it is negative.. (c) Use a graphing utility to compute the root ofx3 8x 5 0. (Do this either by repeatedly zoomingin on the x-intercept of the graph or by using aSOLVE key.)(d) Use the general formula given on page 928 to computethe root of x3 8x 5 0. Check that the answeragrees with the value you obtained in part (c).24