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x^2+2x-3

x^2+2x-3 equation

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Numerical solution:

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The solution

You have entered [src] 
 2              
x  + 2*x - 3 = 0
x2+2x−3=0x^{2} + 2 x - 3 = 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=2b = 2
c=−3c = -3
, then
D = b^2 - 4 * a * c = 

(2)^2 - 4 * (1) * (-3) = 16

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
Simplify
x2=−3x_{2} = -3
Simplify
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=2p = 2
q=caq = \frac{c}{a}
q=−3q = -3
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−2x_{1} + x_{2} = -2
x1x2=−3x_{1} x_{2} = -3
The graph
05-15-10-51015-200200
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -3
x1=−3x_{1} = -3
Simplify 
x2 = 1
x2=1x_{2} = 1
Simplify
Sum and product of roots [src] 
sum
0 - 3 + 1
(−3+0)+1\left(-3 + 0\right) + 1 
=
-2
−2-2 
product
1*-3*1
1(−3)11 \left(-3\right) 1 
=
-3
−3-3 
-3
Numerical answer [src] 
x1 = 1.0
x2 = -3.0
x2 = -3.0
The graph
x^2+2x-3 equation
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