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2*x^2-x-1=0

2*x^2-x-1=0 equation

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Numerical solution:

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The solution

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2*x  - x - 1 = 0
(2x2−x)−1=0\left(2 x^{2} - x\right) - 1 = 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=2a = 2
b=−1b = -1
c=−1c = -1
, then
D = b^2 - 4 * a * c = 

(-1)^2 - 4 * (2) * (-1) = 9

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

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

or
x1=1x_{1} = 1
x2=−12x_{2} = - \frac{1}{2}
Vieta's Theorem
rewrite the equation
(2x2−x)−1=0\left(2 x^{2} - x\right) - 1 = 0
of
ax2+bx+c=0a x^{2} + b x + c = 0
as reduced quadratic equation
x2+bxa+ca=0x^{2} + \frac{b x}{a} + \frac{c}{a} = 0
x2−x2−12=0x^{2} - \frac{x}{2} - \frac{1}{2} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−12p = - \frac{1}{2}
q=caq = \frac{c}{a}
q=−12q = - \frac{1}{2}
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=12x_{1} + x_{2} = \frac{1}{2}
x1x2=−12x_{1} x_{2} = - \frac{1}{2}
The graph
05-15-10-51015-250250
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
1 - 1/2
−12+1- \frac{1}{2} + 1 
=
1/2
12\frac{1}{2} 
product
-1/2
−12- \frac{1}{2} 
=
-1/2
−12- \frac{1}{2} 
-1/2
Rapid solution [src] 
x1 = -1/2
x1=−12x_{1} = - \frac{1}{2} 
x2 = 1
x2=1x_{2} = 1 
x2 = 1
Numerical answer [src] 
x1 = 1.0
x2 = -0.5
x2 = -0.5
The graph
2*x^2-x-1=0 equation
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