What is (2x^2-13x-27)(x^2-2x+6)<= 0 ?

The solution to (2x^2-13x-27)(x^2-2x+6)<= 0 is (13-sqrt(385))/4 <= x<= (13+sqrt(385))/4

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(2x^2-13x-27)(x^2-2x+6)<= 0

(2 x^{2} - 13 x - 27) (x^{2} - 2 x + 6) \leq 0

\frac{13 - 385}{4} \leq x \leq \frac{13 + 385}{4}

Interval Notation

[\frac{13 - 385}{4}, \frac{13 + 385}{4}]

Decimal Notation

- 1.65535 \dots \leq x \leq 8.15535 \dots

Solution steps

(2 x^{2} - 13 x - 27) (x^{2} - 2 x + 6) \leq 0

Factor

2 x^{2} - 13 x - 27 : (x - \frac{13 + 385}{4}) (x - \frac{13 - 385}{4})

(x - \frac{13 + 385}{4}) (x - \frac{13 - 385}{4}) (x^{2} - 2 x + 6) \leq 0

Identify the intervals

\frac{13 - 385}{4} \leq x \leq \frac{13 + 385}{4}

x^{2} - 3 x + 4 > - 2

\frac{- 1}{2 x} > 6

\frac{( x ^{3} + x ^{2} + x )}{( 9 x ^{2} - 25 )} \geq 0

(5 - x) \cdot (2 x - 6) > 0

2 x^{3} - 3 x^{2} + 7 x - 3 > 0

What is (2x^2-13x-27)(x^2-2x+6)<= 0 ?
The solution to (2x^2-13x-27)(x^2-2x+6)<= 0 is (13-sqrt(385))/4 <= x<= (13+sqrt(385))/4