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k^2+4=0

k^2+4=0 equation

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Numerical solution:

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The solution

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 2        
k  + 4 = 0
k2+4=0k^{2} + 4 = 0
Simplify
Detail solution
This equation is of the form
a*k^2 + b*k + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
k1=D−b2ak_{1} = \frac{\sqrt{D} - b}{2 a}
k2=−D−b2ak_{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=4c = 4
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1) * (4) = -16

Because D<0, then the equation
has no real roots,
but complex roots is exists.
k1 = (-b + sqrt(D)) / (2*a)

k2 = (-b - sqrt(D)) / (2*a)

or
k1=2ik_{1} = 2 i
Simplify
k2=−2ik_{2} = - 2 i
Simplify
Vieta's Theorem
it is reduced quadratic equation
k2+kp+q=0k^{2} + k p + q = 0
where
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=4q = 4
Vieta Formulas
k1+k2=−pk_{1} + k_{2} = - p
k1k2=qk_{1} k_{2} = q
k1+k2=0k_{1} + k_{2} = 0
k1k2=4k_{1} k_{2} = 4
The graph
012345-5-4-3-2-1020
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
k1 = -2*I
k1=−2ik_{1} = - 2 i
Simplify 
k2 = 2*I
k2=2ik_{2} = 2 i
Simplify
Sum and product of roots [src] 
sum
0 - 2*I + 2*I
(0−2i)+2i\left(0 - 2 i\right) + 2 i 
=
0
00 
product
1*-2*I*2*I
2i1(−2i)2 i 1 \left(- 2 i\right) 
=
4
44 
4
Numerical answer [src] 
k1 = -2.0*i
k2 = 2.0*i
k2 = 2.0*i
The graph
k^2+4=0 equation
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