What is 4x^4+4x^3-9x^2-x+2<= 0 ?

The solution to 4x^4+4x^3-9x^2-x+2<= 0 is -2<= x<=-1/2 \lor 1/2 <= x<= 1

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4x^4+4x^3-9x^2-x+2<= 0

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

- 2 \leq x \leq - \frac{1}{2} or \frac{1}{2} \leq x \leq 1

Interval Notation

[- 2, - \frac{1}{2}] \cup [\frac{1}{2}, 1]

Decimal Notation

- 2 \leq x \leq - 0.5 or 0.5 \leq x \leq 1

Solution steps

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

Factor

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

(x - 1) (x + 2) (2 x + 1) (2 x - 1) \leq 0

Identify the intervals

- 2 \leq x \leq - \frac{1}{2} or \frac{1}{2} \leq x \leq 1

8 x^{2} + 17 x + 2 = 0

2 x^{2} + 8 x - 18 = 0

\frac{3}{8} p = 9

(x + 2)^{2} = 28

- 5 < x \leq 4

What is 4x^4+4x^3-9x^2-x+2<= 0 ?
The solution to 4x^4+4x^3-9x^2-x+2<= 0 is -2<= x<=-1/2 \lor 1/2 <= x<= 1