I dont really understand this question, can anyone help me out?

Find the condition that the zeros of the polynomial f(x) = x^3+3px^2+3px+r may be in a.p.

Adoughnut shop charges $0.50 for each doughnut and $1 for a carryout box. shirley has $10 to spend. which inequality can be used to find d, the number of doughnuts she could have bought if she also wants them in one carryout box?

Arandom sample of n = 25 observations is taken from a n(µ, σ ) population. a 95% confidence interval for µ was calculated to be (42.16, 57.84). the researcher feels that this interval is too wide. you want to reduce the interval to a width at most 12 units. a) for a confidence level of 95%, calculate the smallest sample size needed. b) for a sample size fixed at n = 25, calculate the largest confidence level 100(1 − α)% needed.