Solve the following polynomial inequalities.
A) x^3 - 5x^2 + 2x ≥ -8
B)2(x3 - 2x2 + 3) < x(x - 1)(x + 1)
x^3 - 5x^2 + 2x ≥ -8
x^3 - 5x^2 + 2x + 8 >= 0
consider the equality:
(x+1)(x-2)(x-4) = 0
Knowing the general shape of cubics, you can surmise that the inequality is satisfied between the first two roots, and beyond the third. So,
-1 <= x < 2 or x >= 4
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in a similar fashion,
x^3 - 4x^2 + x + 6 < 0
(x+1)(x-2)(x-3) < 0
again, negative before 1st root, and between 2nd & 3rd roots
x < -1 or 2<x<3