math (double checking)
posted by Anonymous .
I've posted this question before but I forgot to say that I was dealing with polynomial inequalities (not sure if that makes a difference)
The question is: Solve the following polynomial inequalities. (9 marks)
4x  5 ≤ 2(x  7)
x^3  5x^2 + 2x ≥ 8
2(x^3  2x^2 + 3) < x(x  1)(x + 1)
The answer Reiny previously gave me is the following and I just wanted to double check it:
1.
4x  5 ≤ 2x  14
x ≤ 9
x ≥ 9
2.
x^3  5x^2 + 2x + 8 ≥ 0
(x4)(x2)(x+1) ≥ 0
critical values are x = 4,2, and 1
the graph of f(x) = (x4)(x2)(x+1)
lies above the xaxis between 1 and 2, and values > 4
so 1 ≤ x ≤ 2 OR x ≥ 4
3.
2x^3  4x^2 + 6 < x^3  x
x^3  4x^2 + x + 6 < 0
This expression also factors,
hint: (x+1) is a factor
I will let you finish it, let me know what you got
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