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Solving inequalities/ 1/4x^2>0

1/4x^2>0 inequation

A inequation with variable

The solution

You have entered [src] 
 2    
x     
-- > 0
4
x24>0\frac{x^{2}}{4} > 0 
x^2/4 > 0
Detail solution
Given the inequality:
x24>0\frac{x^{2}}{4} > 0
To solve this inequality, we must first solve the corresponding equation:
x24=0\frac{x^{2}}{4} = 0
Solve:
This equation is of the form
a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=14a = \frac{1}{4}
b=0b = 0
c=0c = 0
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1/4) * (0) = 0

Because D = 0, then the equation has one root.
x = -b/2a = -0/2/(1/4)

x1=0x_{1} = 0
x1=0x_{1} = 0
x1=0x_{1} = 0
This roots
x1=0x_{1} = 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}
=
−110- \frac{1}{10}
=
−110- \frac{1}{10}
substitute to the expression
x24>0\frac{x^{2}}{4} > 0
(−110)24>0\frac{\left(- \frac{1}{10}\right)^{2}}{4} > 0
1/400 > 0

the solution of our inequality is:
x<0x < 0
 _____          
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       x1
Solving inequality on a graph
-5.0-4.0-3.0-2.0-1.05.00.01.02.03.04.00.000.50
Rapid solution 2 [src] 
(-oo, 0) U (0, oo)
x in (−∞,0)∪(0,∞)x\ in\ \left(-\infty, 0\right) \cup \left(0, \infty\right) 
x in Union(Interval.open(-oo, 0), Interval.open(0, oo))
Rapid solution [src] 
And(x > -oo, x < oo, x != 0)
x>−∞∧x<∞∧x≠0x > -\infty \wedge x < \infty \wedge x \neq 0 
(x > -oo)∧(x < oo)∧(Ne(x, 0))
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