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28 May, 07:29

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.

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  1. 28 May, 07:53
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    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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