Write the set of values of x satisfying the inequation $(x^{3} - 2 x + 1) (x - 4) \geq 0$ .

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Solution

$(x^{3} - 2 x + 1) (x - 4) < 0 \Rightarrow (x - 1)^{2} (x - 4) < 0 (x - 1)^{2} i s p o s i t i v e f o r a l l x \neq 1 (x - 1)^{2} = 0 f o r x = 0 (x - 4) i s p o s i t i v e f o r a l l x > 4 (x - 4) i s p o s i t i v e f o r a l l x < 4 (x - 4) = 0 f o r x = 0 (x - 1)^{2} (x - 4) < 0 f o r a l l x < 4 Hence the solution set of the given inequation i s (- \infty, 4)$ .

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