What is 12r^4-16r^3-41r^2+69r-18>0 ?

The solution to 12r^4-16r^3-41r^2+69r-18>0 is r 3/2

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12r^4-16r^3-41r^2+69r-18>0

12 r^{4} - 16 r^{3} - 41 r^{2} + 69 r - 18 > 0

r < - 2 or \frac{1}{3} < r < \frac{3}{2} or r > \frac{3}{2}

Interval Notation

(- \infty, - 2) \cup (\frac{1}{3}, \frac{3}{2}) \cup (\frac{3}{2}, \infty)

Decimal Notation

r < - 2 or 0.33333 \dots < r < 1.5 or r > 1.5

Solution steps

12 r^{4} - 16 r^{3} - 41 r^{2} + 69 r - 18 > 0

Factor

12 r^{4} - 16 r^{3} - 41 r^{2} + 69 r - 18 : (r + 2) (2 r - 3)^{2} (3 r - 1)

(r + 2) (2 r - 3)^{2} (3 r - 1) > 0

Identify the intervals

r < - 2 or \frac{1}{3} < r < \frac{3}{2} or r > \frac{3}{2}

2 x = \frac{1}{4}

x^{2} + 7 x - 1 = 0

x^{2} - 16 x + 58 = 0

4 x^{2} + 4 x - 168 = 0

\frac{y ^{2}}{y ^{- 5}}

What is 12r^4-16r^3-41r^2+69r-18>0 ?
The solution to 12r^4-16r^3-41r^2+69r-18>0 is r<-2\lor 1/3 <r< 3/2 \lor r> 3/2