find all zeroes of polynomial x^4+x^3-9x^2-3x+18 if two of zeroes are -root 3and root 3

Question

solve this....

Answer 1

Given two roots we have (x-√3)(x+√3)=x²-3 is a factor of the polynomial. Divide by this factor:

          x² + x - 6      

x²-3 ) x⁴ + x³ - 9x² - 3x + 18

          x⁴        - 3x²

                 x³ - 6x² - 3x + 18

                 x³          - 3x

                     - 6x²        + 18

                     - 6x²        + 18

                                          0

The quotient factorises: (x+3)(x-2), so the zeroes are -3, -√3, √3, 2.