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k^2-5*k+6=0

k^2-5*k+6=0 equation

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Numerical solution:

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The solution

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 2              
k  - 5*k + 6 = 0
(k2−5k)+6=0\left(k^{2} - 5 k\right) + 6 = 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=−5b = -5
c=6c = 6
, then
D = b^2 - 4 * a * c = 

(-5)^2 - 4 * (1) * (6) = 1

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

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

or
k1=3k_{1} = 3
k2=2k_{2} = 2
Vieta's Theorem
it is reduced quadratic equation
k2+kp+q=0k^{2} + k p + q = 0
where
p=bap = \frac{b}{a}
p=−5p = -5
q=caq = \frac{c}{a}
q=6q = 6
Vieta Formulas
k1+k2=−pk_{1} + k_{2} = - p
k1k2=qk_{1} k_{2} = q
k1+k2=5k_{1} + k_{2} = 5
k1k2=6k_{1} k_{2} = 6
The graph
-10.0-7.5-5.0-2.50.02.55.07.510.012.515.017.5200-100
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
2 + 3
2+32 + 3 
=
5
55 
product
2*3
2⋅32 \cdot 3 
=
6
66 
6
Rapid solution [src] 
k1 = 2
k1=2k_{1} = 2 
k2 = 3
k2=3k_{2} = 3 
k2 = 3
Numerical answer [src] 
k1 = 3.0
k2 = 2.0
k2 = 2.0
The graph
k^2-5*k+6=0 equation
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