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121p²+14p+2=0 equation

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     2               
121*p  + 14*p + 2 = 0
(121p2+14p)+2=0\left(121 p^{2} + 14 p\right) + 2 = 0
Simplify
Detail solution
This equation is of the form
a*p^2 + b*p + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
p1=D−b2ap_{1} = \frac{\sqrt{D} - b}{2 a}
p2=−D−b2ap_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=121a = 121
b=14b = 14
c=2c = 2
, then
D = b^2 - 4 * a * c = 

(14)^2 - 4 * (121) * (2) = -772

Because D<0, then the equation
has no real roots,
but complex roots is exists.
p1 = (-b + sqrt(D)) / (2*a)

p2 = (-b - sqrt(D)) / (2*a)

or
p1=−7121+193i121p_{1} = - \frac{7}{121} + \frac{\sqrt{193} i}{121}
p2=−7121−193i121p_{2} = - \frac{7}{121} - \frac{\sqrt{193} i}{121}
Vieta's Theorem
rewrite the equation
(121p2+14p)+2=0\left(121 p^{2} + 14 p\right) + 2 = 0
of
ap2+bp+c=0a p^{2} + b p + c = 0
as reduced quadratic equation
p2+bpa+ca=0p^{2} + \frac{b p}{a} + \frac{c}{a} = 0
p2+14p121+2121=0p^{2} + \frac{14 p}{121} + \frac{2}{121} = 0
2p2+q=02 p^{2} + q = 0
where
p=bap = \frac{b}{a}
p=14121p = \frac{14}{121}
q=caq = \frac{c}{a}
q=2121q = \frac{2}{121}
Vieta Formulas
p1+p2=−pp_{1} + p_{2} = - p
p1p2=qp_{1} p_{2} = q
p1+p2=−14121p_{1} + p_{2} = - \frac{14}{121}
p1p2=2121p_{1} p_{2} = \frac{2}{121}
Rapid solution [src] 
                 _____
        7    I*\/ 193 
p1 = - --- - ---------
       121      121
p1=−7121−193i121p_{1} = - \frac{7}{121} - \frac{\sqrt{193} i}{121} 
                 _____
        7    I*\/ 193 
p2 = - --- + ---------
       121      121
p2=−7121+193i121p_{2} = - \frac{7}{121} + \frac{\sqrt{193} i}{121} 
p2 = -7/121 + sqrt(193)*i/121
Sum and product of roots [src] 
sum
            _____               _____
   7    I*\/ 193       7    I*\/ 193 
- --- - --------- + - --- + ---------
  121      121        121      121
(−7121−193i121)+(−7121+193i121)\left(- \frac{7}{121} - \frac{\sqrt{193} i}{121}\right) + \left(- \frac{7}{121} + \frac{\sqrt{193} i}{121}\right) 
=
-14 
----
121
−14121- \frac{14}{121} 
product
/            _____\ /            _____\
|   7    I*\/ 193 | |   7    I*\/ 193 |
|- --- - ---------|*|- --- + ---------|
\  121      121   / \  121      121   /
(−7121−193i121)(−7121+193i121)\left(- \frac{7}{121} - \frac{\sqrt{193} i}{121}\right) \left(- \frac{7}{121} + \frac{\sqrt{193} i}{121}\right) 
=
2/121
2121\frac{2}{121} 
2/121
Numerical answer [src] 
p1 = -0.0578512396694215 + 0.114813586689668*i
p2 = -0.0578512396694215 - 0.114813586689668*i
p2 = -0.0578512396694215 - 0.114813586689668*i
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