What is 2x^3+4x^2-24x+18>= 0 ?

The solution to 2x^3+4x^2-24x+18>= 0 is (-3-3sqrt(5))/2 = (3sqrt(5)-3)/2

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2x^3+4x^2-24x+18>= 0

2 x^{3} + 4 x^{2} - 24 x + 18 \geq 0

\frac{- 3 - 3 5}{2} \leq x \leq 1 or x \geq \frac{3 5 - 3}{2}

Interval Notation

[\frac{- 3 - 3 5}{2}, 1] \cup [\frac{3 5 - 3}{2}, \infty)

Decimal Notation

- 4.85410 \dots \leq x \leq 1 or x \geq 1.85410 \dots

Solution steps

2 x^{3} + 4 x^{2} - 24 x + 18 \geq 0

Rewrite in standard form

x^{3} + 2 x^{2} - 12 x + 9 \geq 0

Factor

x^{3} + 2 x^{2} - 12 x + 9 : (x - 1) (x - \frac{- 3 + 3 5}{2}) (x - \frac{- 3 - 3 5}{2})

(x - 1) (x - \frac{- 3 + 3 5}{2}) (x - \frac{- 3 - 3 5}{2}) \geq 0

Identify the intervals

\frac{- 3 - 3 5}{2} \leq x \leq 1 or x \geq \frac{3 5 - 3}{2}

(x - 5) (x - 6) \leq 0

4 (x - 2) (x - 3) \leq 2 (x^{2} - 4)

x^{2} + 1 + (x + 1) 2 < 0

\frac{( ( x - 3 ) ( x - 5 ) )}{( x + 1 )} \leq 0

(x - 5)^{2} < 0

What is 2x^3+4x^2-24x+18>= 0 ?
The solution to 2x^3+4x^2-24x+18>= 0 is (-3-3sqrt(5))/2 <= x<= 1\lor x>= (3sqrt(5)-3)/2