Solve polynomial equation when sum of 2 roots is equal to sum of the other 2 roots?

x^4 - 8x^3 - 14x^2 + 8x -15

let 4 roots be a,b,c,d

sum of 4 roots = 8

sum of 2 roots say ( a+ b) = (c+d) so (a+b)= (c+d) = 4

(x-a)(x-b)(x-c)(x-d) = 0

(x^2 - (a+b) x + ab)(x^2 - (c+d)x + cd) = 0

or (x^2 - 4x + ab)(x^2- 4x+ cd) = 0

say ab = m and cd= n

we get (x^2-4x + m)(x^2 - 4x + n)
= x^4 - 8x^3 + x^2(m + n + 16) - 4x(m+n) + mn

so mn = - 15, m+ n = - 2 , m+n+16 = - 14 (from coefficient)

so equations are consistent

solving we get m = - 5, n = 3

we get (x^4- 4x - 5)(x^2 - 4x + 3)

= (x-5)(x+1) (x-3)(x-1)