What is 2x^3+4x^2-13x+7<0 ?

The solution to 2x^3+4x^2-13x+7<0 is x<-(3+sqrt(23))/2 \lor (sqrt(23)-3)/2 <x<1

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2x^3+4x^2-13x+7<0

2 x^{3} + 4 x^{2} - 13 x + 7 < 0

x < - \frac{3 + 23}{2} or \frac{23 - 3}{2} < x < 1

Interval Notation

(- \infty, - \frac{3 + 23}{2}) \cup (\frac{23 - 3}{2}, 1)

Decimal Notation

x < - 3.89791 \dots or 0.89791 \dots < x < 1

Solution steps

2 x^{3} + 4 x^{2} - 13 x + 7 < 0

Factor

2 x^{3} + 4 x^{2} - 13 x + 7 : (x - 1) (x - \frac{- 3 + 23}{2}) (x + \frac{3 + 23}{2})

(x - 1) (x - \frac{- 3 + 23}{2}) (x + \frac{3 + 23}{2}) < 0

Identify the intervals

x < - \frac{3 + 23}{2} or \frac{23 - 3}{2} < x < 1

x^{3} \geq x^{2}

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

(\frac{5}{3}) < \frac{( 2 x + 1 )}{x}

\frac{( x - 3 )}{( x + 1 )} \geq 0

\frac{( x - 5 )}{( ( x ^{2} + x + 5 ) ( x ^{2} - 4 x - 5 ) )} > 0

What is 2x^3+4x^2-13x+7<0 ?
The solution to 2x^3+4x^2-13x+7<0 is x<-(3+sqrt(23))/2 \lor (sqrt(23)-3)/2 <x<1