We have Int[ 4x^4 + 6x dx] = 10

=> 4*x^4 / 4 + 6x^2 / 2 = 10

=> x^4 + 3x^2 = 10

Let y = x^2

=> y^2 + 3y - 10 = 0

y1 = -3/2 + sqrt (49)/2

=> y1 = -3/2 + 7/2

=> y1 = 2

y2 = -3/2 - 7/2

=> y2 = -5

Now y = x^2

So, we have:

x1 = sqrt 2

x2 = -sqrt 2

x3 = i*sqrt 5

x4 = -i*sqrt 5

**The real and complex roots are { sqrt 2, -sqrt 2, i*sqrt 5, -i*sqrt 5}**