What is x^5-7x^4+13x^3-x^2-14x+8<= 0 ?

The solution to x^5-7x^4+13x^3-x^2-14x+8<= 0 is x<=-1\lor x=1\lor 2<= x<= 4

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x^5-7x^4+13x^3-x^2-14x+8<= 0

x^{5} - 7 x^{4} + 13 x^{3} - x^{2} - 14 x + 8 \leq 0

x \leq - 1 or x = 1 or 2 \leq x \leq 4

Interval Notation

(- \infty, - 1] \cup x = 1 \cup [2, 4]

Solution steps

x^{5} - 7 x^{4} + 13 x^{3} - x^{2} - 14 x + 8 \leq 0

Factor

x^{5} - 7 x^{4} + 13 x^{3} - x^{2} - 14 x + 8 : (x + 1) (x - 1)^{2} (x - 2) (x - 4)

(x + 1) (x - 1)^{2} (x - 2) (x - 4) \leq 0

Identify the intervals

x \leq - 1 or x = 1 or 2 \leq x \leq 4

\frac{x}{( x ^{2} - 3 x - 4 )} > 0

\frac{1}{( x + 1 )} - \frac{1}{x} \leq \frac{1}{( x - 1 )} - \frac{1}{( x - 2 )}

\frac{( x ^{2} + 6 )}{( 5 x )} \geq 1

\frac{4}{( ( x - 2 ) ^{2} )} > 1

(x^{2} - x) (x^{3} - x) (x^{4} - x) < 0

What is x^5-7x^4+13x^3-x^2-14x+8<= 0 ?
The solution to x^5-7x^4+13x^3-x^2-14x+8<= 0 is x<=-1\lor x=1\lor 2<= x<= 4