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x^2-11*x+10=0

x^2-11*x+10=0 equation

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Numerical solution:

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The solution

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x  - 11*x + 10 = 0
(x2−11x)+10=0\left(x^{2} - 11 x\right) + 10 = 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=−11b = -11
c=10c = 10
, then
D = b^2 - 4 * a * c = 

(-11)^2 - 4 * (1) * (10) = 81

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
x1=10x_{1} = 10
x2=1x_{2} = 1
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−11p = -11
q=caq = \frac{c}{a}
q=10q = 10
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=11x_{1} + x_{2} = 11
x1x2=10x_{1} x_{2} = 10
The graph
05-10-53010152025-250250
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
1 + 10
1+101 + 10 
=
11
1111 
product
10
1010 
=
10
1010 
10
Rapid solution [src] 
x1 = 1
x1=1x_{1} = 1 
x2 = 10
x2=10x_{2} = 10 
x2 = 10
Numerical answer [src] 
x1 = 1.0
x2 = 10.0
x2 = 10.0
The graph
x^2-11*x+10=0 equation
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