If two zeros of the polynomial f(x) = x⁴ - 6x³ - 26x² + 138x - 35 are 2 ± √3.Find the other zeros.     (Ans:7, -5)

Ans: Let the two zeros are 2 +√3 and 2 - √3

Sum of Zeros       = 2 + √3 + 2 - √3

= 4

Product of Zeros = ( 2+√3 )(2 - √3 )

= 4 - 3

= 1

Quadratic polynomial is x² - (sum) x + Product

                  x⁴ - 4 x³ + 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