Mister Exam

Other calculators

x^2+3=0

x^2+3=0 equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src] 
 2        
x  + 3 = 0
$$x^{2} + 3 = 0$$
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:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 0$$
$$c = 3$$
, 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
$$x_{1} = \sqrt{3} i$$
$$x_{2} = - \sqrt{3} i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 3$$
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
          ___
x1 = -I*\/ 3
$$x_{1} = - \sqrt{3} i$$ 
         ___
x2 = I*\/ 3
$$x_{2} = \sqrt{3} i$$ 
x2 = sqrt(3)*i
Sum and product of roots [src] 
sum
      ___       ___
- I*\/ 3  + I*\/ 3
$$- \sqrt{3} i + \sqrt{3} i$$ 
=
0
$$0$$ 
product
     ___     ___
-I*\/ 3 *I*\/ 3
$$- \sqrt{3} i \sqrt{3} i$$ 
=
3
$$3$$ 
3
Numerical answer [src] 
x1 = 1.73205080756888*i
x2 = -1.73205080756888*i
x2 = -1.73205080756888*i
The graph
x^2+3=0 equation
    © Mister Exam – Calculator