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Amy solved the equation 2x ^ 2 + 5x - 42 = 0 She stated that the solutions to the equation were 7/2 and -6. Do you agree with Amy's solutions? Explain why or why not.

Respuesta :

joseaaronlara

Answer:

The answer to your question is Amy is correct.

Step-by-step explanation:

Data

Equation              2x² + 5x - 42 = 0

-Factor

 2 x 42 = 84

- Find the prime factors of 84

                                       84     2

                                       42     2

                                        21     3

                                          7     7

                                           1

84 = 2² 3 7

-Find two numbers that added gives 5

 These numbers are 12 and -7

- Express the equation using these numbers

                          2x² + 12x - 7x - 42

-Factor by common factor

                          2x(x + 6) -7(x + 6)

-Factor by grouping

                              (x + 6)(2x - 7)

-Find the roots

                        x₁ + 6 = 0            2x₂ - 7 = 0

                        x₁ = -6                 2x₂ = 7

                                                     x₂ = 7/2

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