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Solving inequalities/ z^2+5*z<0

z^2+5*z<0 inequation

A inequation with variable

The solution

You have entered [src] 
 2          
z  + 5*z < 0
z2+5z<0z^{2} + 5 z < 0 
z^2 + 5*z < 0
Detail solution
Given the inequality:
z2+5z<0z^{2} + 5 z < 0
To solve this inequality, we must first solve the corresponding equation:
z2+5z=0z^{2} + 5 z = 0
Solve:
x1=−5x_{1} = -5
x2=0x_{2} = 0
x1=−5x_{1} = -5
x2=0x_{2} = 0
This roots
x1=−5x_{1} = -5
x2=0x_{2} = 0
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
x0<x1x_{0} < x_{1}
For example, let's take the point
x0=x1−110x_{0} = x_{1} - \frac{1}{10}
=
−5+−110-5 + - \frac{1}{10}
=
−5.1-5.1
substitute to the expression
z2+5z<0z^{2} + 5 z < 0
z2+5z<0z^{2} + 5 z < 0
 2          
z  + 5*z < 0

Then
x<−5x < -5
no execute
one of the solutions of our inequality is:
x>−5∧x<0x > -5 \wedge x < 0
         _____  
        /     \  
-------ο-------ο-------
       x1      x2
Rapid solution [src] 
And(-5 < z, z < 0)
−5<z∧z<0-5 < z \wedge z < 0 
(-5 < z)∧(z < 0)
Rapid solution 2 [src] 
(-5, 0)
x in (−5,0)x\ in\ \left(-5, 0\right) 
x in Interval.open(-5, 0)
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