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x^2+3=0

x^2+3=0 equation

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Numerical solution:

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The solution

You have entered [src] 
 2        
x  + 3 = 0
x2+3=0x^{2} + 3 = 0
Simplify
Detail solution
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=0b = 0
c=3c = 3
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1) * (3) = -12

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=3ix_{1} = \sqrt{3} i
x2=−3ix_{2} = - \sqrt{3} i
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=3q = 3
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=0x_{1} + x_{2} = 0
x1x2=3x_{1} x_{2} = 3
The graph
012345-5-4-3-2-1020
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
          ___
x1 = -I*\/ 3
x1=−3ix_{1} = - \sqrt{3} i 
         ___
x2 = I*\/ 3
x2=3ix_{2} = \sqrt{3} i 
x2 = sqrt(3)*i
Sum and product of roots [src] 
sum
      ___       ___
- I*\/ 3  + I*\/ 3
−3i+3i- \sqrt{3} i + \sqrt{3} i 
=
0
00 
product
     ___     ___
-I*\/ 3 *I*\/ 3
−3i3i- \sqrt{3} i \sqrt{3} i 
=
3
33 
3
Numerical answer [src] 
x1 = 1.73205080756888*i
x2 = -1.73205080756888*i
x2 = -1.73205080756888*i
The graph
x^2+3=0 equation
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