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k^2+k=0

k^2+k=0 equation

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Numerical solution:

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The solution

You have entered [src] 
 2        
k  + k = 0
k2+k=0k^{2} + k = 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=1b = 1
c=0c = 0
, then
D = b^2 - 4 * a * c = 

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

Because D > 0, then the equation has two roots.
k1 = (-b + sqrt(D)) / (2*a)

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

or
k1=0k_{1} = 0
k2=−1k_{2} = -1
Vieta's Theorem
it is reduced quadratic equation
k2+kp+q=0k^{2} + k p + q = 0
where
p=bap = \frac{b}{a}
p=1p = 1
q=caq = \frac{c}{a}
q=0q = 0
Vieta Formulas
k1+k2=−pk_{1} + k_{2} = - p
k1k2=qk_{1} k_{2} = q
k1+k2=−1k_{1} + k_{2} = -1
k1k2=0k_{1} k_{2} = 0
The graph
-15.0-12.5-10.0-7.5-5.0-2.50.02.55.07.515.010.012.5200-100
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-1
−1-1 
=
-1
−1-1 
product
-0
−0- 0 
=
0
00 
0
Rapid solution [src] 
k1 = -1
k1=−1k_{1} = -1 
k2 = 0
k2=0k_{2} = 0 
k2 = 0
Numerical answer [src] 
k1 = 0.0
k2 = -1.0
k2 = -1.0
The graph
k^2+k=0 equation
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