Mister Exam

Other calculators

x^2+11=0

x^2+11=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  + 11 = 0
x2+11=0x^{2} + 11 = 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=11c = 11
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1) * (11) = -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=11ix_{1} = \sqrt{11} i
x2=−11ix_{2} = - \sqrt{11} 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=11q = 11
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=0x_{1} + x_{2} = 0
x1x2=11x_{1} x_{2} = 11
The graph
-4.0-3.0-2.0-1.00.01.02.03.04.0020
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
          ____
x1 = -I*\/ 11
x1=−11ix_{1} = - \sqrt{11} i 
         ____
x2 = I*\/ 11
x2=11ix_{2} = \sqrt{11} i 
x2 = sqrt(11)*i
Sum and product of roots [src] 
sum
      ____       ____
- I*\/ 11  + I*\/ 11
−11i+11i- \sqrt{11} i + \sqrt{11} i 
=
0
00 
product
     ____     ____
-I*\/ 11 *I*\/ 11
−11i11i- \sqrt{11} i \sqrt{11} i 
=
11
1111 
11
Numerical answer [src] 
x1 = -3.3166247903554*i
x2 = 3.3166247903554*i
x2 = 3.3166247903554*i
The graph
x^2+11=0 equation
    © Mister Exam – Calculator