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Solving inequalities/ x^2-2x+12>0

x^2-2x+12>0 inequation

A inequation with variable

The solution

You have entered [src] 
 2               
x  - 2*x + 12 > 0
(x2−2x)+12>0\left(x^{2} - 2 x\right) + 12 > 0 
x^2 - 2*x + 12 > 0
Detail solution
Given the inequality:
(x2−2x)+12>0\left(x^{2} - 2 x\right) + 12 > 0
To solve this inequality, we must first solve the corresponding equation:
(x2−2x)+12=0\left(x^{2} - 2 x\right) + 12 = 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=1a = 1
b=−2b = -2
c=12c = 12
, then
D = b^2 - 4 * a * c = 

(-2)^2 - 4 * (1) * (12) = -44

Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
x1=1+11ix_{1} = 1 + \sqrt{11} i
x2=1−11ix_{2} = 1 - \sqrt{11} i
x1=1+11ix_{1} = 1 + \sqrt{11} i
x2=1−11ix_{2} = 1 - \sqrt{11} i
Exclude the complex solutions:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example
x0 = 0

(02−0⋅2)+12>0\left(0^{2} - 0 \cdot 2\right) + 12 > 0
12 > 0

so the inequality is always executed
Solving inequality on a graph
-5.0-4.0-3.0-2.0-1.05.00.01.02.03.04.0020
Rapid solution 2 [src] 
(-oo, oo)
x in (−∞,∞)x\ in\ \left(-\infty, \infty\right) 
x in Interval(-oo, oo)
Rapid solution [src] 
And(-oo < x, x < oo)
−∞<x∧x<∞-\infty < x \wedge x < \infty 
(-oo < x)∧(x < oo)
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