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Math Help - Quadratic answer evidently wrong (pest of a teacher)

  1. #1
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    Quadratic answer evidently wrong (pest of a teacher)

    After posting all this work, in both formats, my teacher still wants to play games and is asking me what number should be paired with -5 and what number should be paired with 2. What in the world is she talking about?

    1. The product of two numbers is 10. One number is 3 more than the other number. What is the quadratic equation that models these numbers?


    x(x + 3) = 10
    x^2 + 3x - 10 = 0


    2. Solve the quadratic equation from #1, to find the pairs of numbers.


    x = -(3) +_ SQRT((3)^2) - 4(1)(-10)/2(1)


    = -3 +_ SQRT(9 + 40)/2 = -3 +_ SQRT(49)/ 2


    = -3 +_7/2 = -3 - 7/2, -3 + 7/2


    = -10/2, 4/2 = -5, 2


    x = -5, x = 2

    and this additional work:

    (b + 3)b = 10

    b^2 + 3b = 10

    b^2 + 3b -10 = 0

    x = -(3) +_ SQRT((3)^2 - 4(1)(-10)/2(1)

    = -3 +_ SQRT(9 + 40)/2 = -3 +_SQRT(49)/2

    = -3 +_ 7/2 = -3 -7/2, -3 +7/2

    = -10/2, 4/2

    = -5, 2

    x = -5, 2

    I mean, this just seems rediculous
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  2. #2
    Super Member Matt Westwood's Avatar
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    There are two solutions to x (x+3) = 10.

    one is -5, one is 2.

    If you take one of the x's as 2, you see that 2 \times (2+3) = 2 \times 5 = 10. The two numbers are 2 and 5.

    But also, you see you have -5 as the other solution.

    And indeed, you see that -5 \times (-5 + 3) = -5 \times -2 = 10.

    So that's the other pair: -5 and -2.
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  3. #3
    Member SENTINEL4's Avatar
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    Quote Originally Posted by bobbyboy1111 View Post
    After posting all this work, in both formats, my teacher still wants to play games and is asking me what number should be paired with -5 and what number should be paired with 2. What in the world is she talking about?

    1. The product of two numbers is 10. One number is 3 more than the other number. What is the quadratic equation that models these numbers?


    x(x + 3) = 10
    x^2 + 3x - 10 = 0

    If you solve the quadratic equation you find x=-5 and x=2.
    So if x=-5 \Rightarrow x+3 = -5+3 = -2
    and if x=2 \Rightarrow x+3 = 2+3 = 5

    The pairs -5, -2 and 2, 5 give product 10
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  4. #4
    MHF Contributor

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    And you should thank this "pest of a teacher" for requiring you to think about what you are doing rather than just apply rote formulas!
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