This problem has two parts, Part A and Part B.

Part A: Are all of the roots of the polynomial P(x)=x3+3x2−11x−5 rational numbers? Why or why not?

Part B: What are the rational roots of P(x)=x3+3x2−11x−5?

(b) suppose that consolidated power decides to use a level of significance of α = .05, and suppose a random sample of 100 temperature readings is obtained. if the sample mean of the 100 temperature readings is x⎯⎯ = 60.990, test h0 versus ha and determine whether the power plant should be shut down and the cooling system repaired. perform the hypothesis test by using a critical value and a p-value. assume σ = 5. (round your z to 2 decimal places and p-value to 4 decimal places.)