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find the roots of this polynomial equation

x^3-2x^2+10x+136=0

Sagot :

Panoyinidn
                                x³ - 2x² + 10x + 136 = 0
              x³ - 6x² + 4x² + 34x - 24x + 136 = 0
              x³ - 6x² + 34x + 4x² - 24x + 136 = 0
x(x²) - x(6x) + x(34) + 4(x²) - 4(6x) + 4(34) = 0
               x(x² - 6x + 34) + 4(x² - 6x + 34) = 0
                                  (x + 4)(x² - 6x + 34) = 0
                     x + 4 = 0    U    x² - 6x + 34 = 0
                        - 4  - 4           x = -(-6) +/- √((-6)² - 4(1)(34))
                           x = -4                                2(1)
                                              x = 6 +/- √(36 - 136)
                                                                2
                                              x = 6 +/- √(-100)
                                                             2
                                              x = 6 +/- 10i
                                                          2
                                              x = 3 + 5i
                                              x = 3 + 5i    U    x = 3 - 5i
The solution set is equal to {-4, 3 + 5i}.
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