Answer to Question #26165 in Algebra for fatma

Question

Solve the reciprocal equation 6x6-25x5+31x4-31x2+25x-6=0

Answer 1

We can rewrite the equation
(x-2)(x-1)(x+1)(2x-1)(3x^2 - 5x +3)=0
It's possible if one of the factors equals zero. Therefore we obtain the following equation: x-2=0 or x-1=0or x+1=0 or 2x-1=0 or 3x^2 - 5x +3 =0
So we have 4 real solutions and 2 complex.
Real:
x=2
x=1
x=-1
x=1/2
Complex:
x=1/6(5-i*sqrt(11))
x=1/6(5+i*sqrt(11))