Hi i am trying to find the roots of the following equation,
2x4 -8x3 +13x2 -13x + 6 = 0
I know two of the roots shold be x=1 and x=2 and that there should be 2 more roots that are complex but I dont know how to calculate them.
I would do it slightly differently. Rather than multiplying (x- 1)(x- 2) I would use "Synthetic Division" to divide by x- 1 and than again use synthetic division to divide the result by x- 2. That leaves a quadratic equation which can be solved by the quadratic formula.
Let the four roots be 1, 2, a+ib and a-ib.
Sum of the roots = 8/2 = 4 = 3 + 2a.
So a = 1/2.
The product of roots = 2(a^2 + b^2) = 6/2 = 3
a^2 + b^2 = 3/2
b^2 = 3/2-1/4 = 5/4
So b = sqrt(5)/2
So the roots are 1, 2, 1/2 + i*sqrt(5)/2 and 1/2 - i*sqrt(5)/2