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x^2-3x-4=0

x^2-3x-4=0 equation

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Numerical solution:

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The solution

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x  - 3*x - 4 = 0
(x2−3x)−4=0\left(x^{2} - 3 x\right) - 4 = 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=−3b = -3
c=−4c = -4
, then
D = b^2 - 4 * a * c = 

(-3)^2 - 4 * (1) * (-4) = 25

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

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

or
x1=4x_{1} = 4
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=−3p = -3
q=caq = \frac{c}{a}
q=−4q = -4
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=3x_{1} + x_{2} = 3
x1x2=−4x_{1} x_{2} = -4
The graph
05-15-10-5101520-200200
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-1 + 4
−1+4-1 + 4 
=
3
33 
product
-4
−4- 4 
=
-4
−4-4 
-4
Rapid solution [src] 
x1 = -1
x1=−1x_{1} = -1 
x2 = 4
x2=4x_{2} = 4 
x2 = 4
Numerical answer [src] 
x1 = 4.0
x2 = -1.0
x2 = -1.0
The graph
x^2-3x-4=0 equation
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