What is 1/5 x^5-x^4-5/3 x^3>= 0 ?

The solution to 1/5 x^5-x^4-5/3 x^3>= 0 is (15-5sqrt(21))/6 = (15+5sqrt(21))/6

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1/5 x^5-x^4-5/3 x^3>= 0

\frac{1}{5} x^{5} - x^{4} - \frac{5}{3} x^{3} \geq 0

\frac{15 - 5 21}{6} \leq x \leq 0 or x \geq \frac{15 + 5 21}{6}

Interval Notation

[\frac{15 - 5 21}{6}, 0] \cup [\frac{15 + 5 21}{6}, \infty)

Decimal Notation

- 1.31881 \dots \leq x \leq 0 or x \geq 6.31881 \dots

Solution steps

\frac{1}{5} x^{5} - x^{4} - \frac{5}{3} x^{3} \geq 0

Rewrite in standard form

3 x^{5} - 15 x^{4} - 25 x^{3} \geq 0

Factor

3 x^{5} - 15 x^{4} - 25 x^{3} : x^{3} (x - \frac{15 + 5 21}{6}) (x - \frac{15 - 5 21}{6})

x^{3} (x - \frac{15 + 5 21}{6}) (x - \frac{15 - 5 21}{6}) \geq 0

Identify the intervals

\frac{15 - 5 21}{6} \leq x \leq 0 or x \geq \frac{15 + 5 21}{6}

(5 x + 3) \cdot (x - \frac{1}{5}) + 2 = 3

1.2 x = 6

\frac{x - 6}{x - 9} > 0

2 x^{2} - 5 x - 52 = 0

2 (4 x - 5) = 7 x

What is 1/5 x^5-x^4-5/3 x^3>= 0 ?
The solution to 1/5 x^5-x^4-5/3 x^3>= 0 is (15-5sqrt(21))/6 <= x<= 0\lor x>= (15+5sqrt(21))/6