What is x^3-10x^2-7x+16>0 ?

The solution to x^3-10x^2-7x+16>0 is (9-sqrt(145))/2 (9+sqrt(145))/2

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x^3-10x^2-7x+16>0

x^{3} - 10 x^{2} - 7 x + 16 > 0

\frac{9 - 145}{2} < x < 1 or x > \frac{9 + 145}{2}

Interval Notation

(\frac{9 - 145}{2}, 1) \cup (\frac{9 + 145}{2}, \infty)

Decimal Notation

- 1.52079 \dots < x < 1 or x > 10.52079 \dots

Solution steps

x^{3} - 10 x^{2} - 7 x + 16 > 0

Factor

x^{3} - 10 x^{2} - 7 x + 16 : (x - 1) (x - \frac{9 + 145}{2}) (x - \frac{9 - 145}{2})

(x - 1) (x - \frac{9 + 145}{2}) (x - \frac{9 - 145}{2}) > 0

Identify the intervals

\frac{9 - 145}{2} < x < 1 or x > \frac{9 + 145}{2}

\frac{( 3 x + 1 )}{( ( 2 x + 5 ) ( 5 x + 3 ) )} > 0

(x + 4)^{5} (x + 3)^{6} (x + 2)^{7} (x - 1)^{8} \leq 0

\frac{( x ^{2} + x - 20 )}{( - x ^{2} + 9 )} > 0

x^{2} - 5 x + 2 < \frac{1}{2}

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

What is x^3-10x^2-7x+16>0 ?
The solution to x^3-10x^2-7x+16>0 is (9-sqrt(145))/2 <x<1\lor x>(9+sqrt(145))/2