What is 4x^3-9x^2-11x+26>= 0 ?

The solution to 4x^3-9x^2-11x+26>= 0 is (1-sqrt(209))/8 = 2

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4x^3-9x^2-11x+26>= 0

4 x^{3} - 9 x^{2} - 11 x + 26 \geq 0

\frac{1 - 209}{8} \leq x \leq \frac{1 + 209}{8} or x \geq 2

Interval Notation

[\frac{1 - 209}{8}, \frac{1 + 209}{8}] \cup [2, \infty)

Decimal Notation

- 1.68210 \dots \leq x \leq 1.93210 \dots or x \geq 2

Solution steps

4 x^{3} - 9 x^{2} - 11 x + 26 \geq 0

Factor

4 x^{3} - 9 x^{2} - 11 x + 26 : (x - 2) (x - \frac{1 + 209}{8}) (x - \frac{1 - 209}{8})

(x - 2) (x - \frac{1 + 209}{8}) (x - \frac{1 - 209}{8}) \geq 0

Identify the intervals

\frac{1 - 209}{8} \leq x \leq \frac{1 + 209}{8} or x \geq 2

x^{2} + x + 3 < 0

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

(x - 4) (x + 5) > 0

\frac{1}{( 2 x + 1 )} > 0

2 x^{2} - 2 x + 3 > 0

What is 4x^3-9x^2-11x+26>= 0 ?
The solution to 4x^3-9x^2-11x+26>= 0 is (1-sqrt(209))/8 <= x<= (1+sqrt(209))/8 \lor x>= 2