What are the zeros of the function f ( x ) = x 2 + 5 x + 5 written in simplest radical form?

Question

What are the zeros of the function             f              (        x        )              =          x      2        +    5    x    +    5    written in simplest radical form?

Bruno Stanley · Accepted Answer

We have:            f              (        x        )              =          x      2        +    5    x    +    5  Method 1 - Completing the squareSolve:      0    =    4          f              (        x        )                                0              =    4          (              x        2            +      5      x      +      5      )                          0              =    4          x      2        +    20    x    +    20                      0              =                  (        2        x        )            2        +    2          (      2      x      )              (      5      )        +    25    -    5                      0              =                  (        2        x        +        5        )            2        -                  (                              5                          )            2                          0              =          (              (        2        x        +        5        )            -                        5                    )              (              (        2        x        +        5        )            +                        5                    )                          0              =          (      2      x      +      5      -                        5                    )              (      2      x      +      5      +                        5                    )      Then:      2    x    =    -    5    ±                  5            Dividing both sides by 2, we find:      x    =    -          5      2        ±                            5                    2

Addison Stuart · Accepted Answer

Method 2 - Quadratic formulaNote that f(x) is in standard quadratic form:            f              (        x        )              =    a          x      2        +    b    x    +    c  with a=1, b=5 and c=5.According to the quadratic formula, this has zeros:      x    =                  -        b        ±                                            b              2                        -            4            a            c                                      2        a                                x              =                  -                  (                                    5                                )                ±                                                            (                                                      5                                                  )                            2                        -            4                          (                                                1                                            )                                      (                                                5                                            )                                                  2                  (                                    1                                )                                        x              =                  -        5        ±                              25            -            20                              2                          x              =                  -        5        ±                              5                              2                          x              =    -          5      2        ±                            5                    2

What are the zeros of the function f ( x ) = x 2 +...

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