What is -2x^4+10x^3-6x^2-18x>= 0 ?

The solution to -2x^4+10x^3-6x^2-18x>= 0 is -1<= x<= 0\lor x=3

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-2x^4+10x^3-6x^2-18x>= 0

- 2 x^{4} + 10 x^{3} - 6 x^{2} - 18 x \geq 0

- 1 \leq x \leq 0 or x = 3

Interval Notation

[- 1, 0] \cup x = 3

Solution steps

- 2 x^{4} + 10 x^{3} - 6 x^{2} - 18 x \geq 0

Rewrite in standard form

- x^{4} + 5 x^{3} - 3 x^{2} - 9 x \geq 0

Factor

- x^{4} + 5 x^{3} - 3 x^{2} - 9 x : - x (x + 1) (x - 3)^{2}

- x (x + 1) (x - 3)^{2} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

(- x (x + 1) (x - 3)^{2}) (- 1) \leq 0 \cdot (- 1)

Simplify

x (x + 1) (x - 3)^{2} \leq 0

Identify the intervals

- 1 \leq x \leq 0 or x = 3

2 x^{2} - 5 x + 2 \leq 0

x^{5} + 12 x^{3}

∣ 5 - 4 x ∣ < 20

\frac{x}{5} - 4 = - 6

\frac{3 y}{10 x ^{3}} + \frac{2}{15 x y}

What is -2x^4+10x^3-6x^2-18x>= 0 ?
The solution to -2x^4+10x^3-6x^2-18x>= 0 is -1<= x<= 0\lor x=3