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k^2-4*k+3=0

k^2-4*k+3=0 equation

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Numerical solution:

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The solution

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 2              
k  - 4*k + 3 = 0
k2−4k+3=0k^{2} - 4 k + 3 = 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=−4b = -4
c=3c = 3
, then
D = b^2 - 4 * a * c = 

(-4)^2 - 4 * (1) * (3) = 4

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
Simplify
k2=1k_{2} = 1
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=−4p = -4
q=caq = \frac{c}{a}
q=3q = 3
Vieta Formulas
k1+k2=−pk_{1} + k_{2} = - p
k1k2=qk_{1} k_{2} = q
k1+k2=4k_{1} + k_{2} = 4
k1k2=3k_{1} k_{2} = 3
The graph
05-10-51015200-100
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
k1 = 1
k1=1k_{1} = 1
Simplify 
k2 = 3
k2=3k_{2} = 3
Simplify
Sum and product of roots [src] 
sum
0 + 1 + 3
(0+1)+3\left(0 + 1\right) + 3 
=
4
44 
product
1*1*3
1⋅1⋅31 \cdot 1 \cdot 3 
=
3
33 
3
Numerical answer [src] 
k1 = 3.0
k2 = 1.0
k2 = 1.0
The graph
k^2-4*k+3=0 equation
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