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3x^2-5x-2=0

3x^2-5x-2=0 equation

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Numerical solution:

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The solution

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3*x  - 5*x - 2 = 0
3x2−5x−2=03 x^{2} - 5 x - 2 = 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=3a = 3
b=−5b = -5
c=−2c = -2
, then
D = b^2 - 4 * a * c = 

(-5)^2 - 4 * (3) * (-2) = 49

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

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

or
x1=2x_{1} = 2
Simplify
x2=−13x_{2} = - \frac{1}{3}
Simplify
Vieta's Theorem
rewrite the equation
3x2−5x−2=03 x^{2} - 5 x - 2 = 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
x2−5x3−23=0x^{2} - \frac{5 x}{3} - \frac{2}{3} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−53p = - \frac{5}{3}
q=caq = \frac{c}{a}
q=−23q = - \frac{2}{3}
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=53x_{1} + x_{2} = \frac{5}{3}
x1x2=−23x_{1} x_{2} = - \frac{2}{3}
The graph
05-15-10-51015-500500
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -1/3
x1=−13x_{1} = - \frac{1}{3}
Simplify 
x2 = 2
x2=2x_{2} = 2
Simplify
Sum and product of roots [src] 
sum
0 - 1/3 + 2
(−13+0)+2\left(- \frac{1}{3} + 0\right) + 2 
=
5/3
53\frac{5}{3} 
product
1*-1/3*2
1(−13)21 \left(- \frac{1}{3}\right) 2 
=
-2/3
−23- \frac{2}{3} 
-2/3
Numerical answer [src] 
x1 = -0.333333333333333
x2 = 2.0
x2 = 2.0
The graph
3x^2-5x-2=0 equation
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