Question

Ecrever uma equaçao do 2 grau cuja raizes sejam -3 e 5

Answer 1

Recordando:

x1 = - b + √b² - 4.a.c

         ____________

                  2a

x2 = - b - √b² - 4ac

        ___________

                2a

x1 + x2 = - b + √b² - 4ac      - b - √b² - 4ac

                 ___________ +  ___________

                          2a                       2a

                - b + √b² - 4ac     -    b - √b² - 4ac

x1 + x2 =   _________________________⇒

                                      2a

x1 + x2 = - 2b

                 __⇒

                 2a

x1 + x2 = - b|a

x1.x2 =( - b + √b² - 4ac)   (- b + √b² - 4ac)

              ___________. _________________⇒

                     2a                        2a

x1.x2 = (-b)² - (√b² - 4ac)²

             ______________⇒

                      4a²

x1.x2 = b² - b² - 4ac

             _________⇒

                  4a²

x1.x2 = - 4ac

              ___⇒

               4a²

x1.x2 = - c|a

Então temos:

x1 = - 3 e x2 = 5

x1 + x2 = -b|a⇒

- 3 + 5 = -b|a⇒

-b|a = 2

-3.5 = -c|a⇒

-15 - -c|a⇒

c|a = 15

1 x² - 2x + 15 = 0

Espero tê-lo ajudado.

Bons Estudos.

kélémen.