Question: Real roots only

January 17 2014 Syeda 25
0

I want to find real roots only.  Cannot we find a simplified formula for x in this case which gives only real roots? 

 

 

``

eq1 := a^2*x^3+Typesetting:-delayDotProduct(2*a*b-Typesetting:-delayDotProduct(a^2, e), x^2)+(-2*a*b*c^2-a*c+b^2)*x-c*b-d-b^2*e = 0:

``

# Formula

eq2 := A*x^3+B*x^2+C*x+E = 0:

``

NULL

a := .7438:

b := 15.12*z[1]+10.85*z[1]^2:

c := 18.92-17.76*z[2]:

d := -.9224:

e := 2.106-5.317*z[2]+2.87*z[2]^2:NULL

NULL

A := a^2:

B := -a^2*e+2*a*b:

C := -2*a*b*e^2-a*c+b^2:

E := -b^2*e-b*c-d:

``

eq2

.55323844*x^3+(-1.165120155+2.941568785*z[2]-1.587794323*z[2]^2+22.492512*z[1]+16.140460*z[1]^2)*x^2+(-1.4876*(15.12*z[1]+10.85*z[1]^2)*(2.106-5.317*z[2]+2.87*z[2]^2)^2-14.072696+13.209888*z[2]+(15.12*z[1]+10.85*z[1]^2)^2)*x-(15.12*z[1]+10.85*z[1]^2)^2*(2.106-5.317*z[2]+2.87*z[2]^2)-(15.12*z[1]+10.85*z[1]^2)*(18.92-17.76*z[2])+.9224 = 0

(1)

``

``# Putting z1 and z2 value

"(->)"

.55323844*x^3+14.11629660*x^2+83.26002702*x-3.52866181 = 0

(2)

 

"(->)"

[[x = 0.4208050385e-1], [x = -9.354079555], [x = -16.20375615]]

(3)

``

``

 

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