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3*x^2+3=0

3*x^2+3=0 equation

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Numerical solution:

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The solution

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3*x  + 3 = 0
3x2+3=03 x^{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=3a = 3
b=0b = 0
c=3c = 3
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (3) * (3) = -36

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=ix_{1} = i
Simplify
x2=−ix_{2} = - i
Simplify
Vieta's Theorem
rewrite the equation
3x2+3=03 x^{2} + 3 = 0
of
ax2+bx+c=0a x^{2} + b x + c = 0
as reduced quadratic equation
x2+bxa+ca=0x^{2} + \frac{b x}{a} + \frac{c}{a} = 0
x2+1=0x^{2} + 1 = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=1q = 1
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=0x_{1} + x_{2} = 0
x1x2=1x_{1} x_{2} = 1
The graph
-3.0-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.53.0020
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -I
x1=−ix_{1} = - i
Simplify 
x2 = I
x2=ix_{2} = i
Simplify
Sum and product of roots [src] 
sum
0 - I + I
(0−i)+i\left(0 - i\right) + i 
=
0
00 
product
1*-I*I
i1(−i)i 1 \left(- i\right) 
=
1
11 
1
Numerical answer [src] 
x1 = 1.0*i
x2 = -1.0*i
x2 = -1.0*i
The graph
3*x^2+3=0 equation
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