What is 2x^4+13x^3+9x^2-40x+16>= 0 ?

The solution to 2x^4+13x^3+9x^2-40x+16>= 0 is x = 1

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2x^4+13x^3+9x^2-40x+16>= 0

2 x^{4} + 13 x^{3} + 9 x^{2} - 40 x + 16 \geq 0

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

Solution steps

2 x^{4} + 13 x^{3} + 9 x^{2} - 40 x + 16 \geq 0

Factor

2 x^{4} + 13 x^{3} + 9 x^{2} - 40 x + 16 : (x - 1) (x + 4)^{2} (2 x - 1)

(x - 1) (x + 4)^{2} (2 x - 1) \geq 0

Identify the intervals

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

3 x - 1 > 5

\frac{1}{2} \cdot 2 π

\frac{1}{3} \cdot \frac{1}{6}

(\frac{8 x ^{6}}{27 y ^{9}})^{\frac{1}{3}}

3 x^{2} + 12 x + 9

What is 2x^4+13x^3+9x^2-40x+16>= 0 ?
The solution to 2x^4+13x^3+9x^2-40x+16>= 0 is x<= 1/2 \lor x>= 1