If two zeros of the polynomial f(x) = x4 - 6x3 - 26x2 + 138x – 35 are 2±√3.Find the other zeros

Ans: Let the two zeros are 2 +
        Sum of Zeros       = 2 +
                = 4
        Product of Zeros = ( 2+
      = 4 – 3
      = 1
     Quadratic polynomial is x2 – (sum) x + Product
    

x2 – 2x – 35 
x2 – 4x + 1 x4 −6x3 −26x2 +138x−35   
x4 −4x3 + x2
           -----------------
                     -2x3 – 27x2 + 138x
- 2x3 + 8x2 – 2x
-----------------------             -35x2 + 140x – 35
             -35x2 + 140x – 35
            ------------------------
                0
           ------------------------ 
∴ x2 – 2x – 35 = 0
    (x – 7)(x + 5) = 0
  x = 7, -5  other two Zeros are 7 and -5