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24 December, 14:29

Which of the following polynomials has zeros at x=-4 and x=7?

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  1. 24 December, 14:58
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    Remark

    This requires that you factor all 4 choices. There is no other way to do it. However you can eliminate one of the choices.

    C might give you a factor of 1/7 but it will not give you 7. The same can be said about a and b. They do factor, but you will get a fraction in both answers. That means your answer is probably D, which we should check out first.

    Solution

    x ^2 - 3x - 28 = 0

    (x - 7) (x + 4) = 0 These factors come about because the numbers 4 and 7 are relatively close together. Your other choices for factors would be 2 and 14 or 1 and 28. These numbers are just too far apart when subtracted to be the answer.

    x - 7 = 0

    x = 7

    x + 4 = 0

    x = - 4

    D is indeed your answer.

    C

    No factors will work. This cannot be factored into integer results.

    B

    4x^2 - 49 Use the difference of squares.

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

    x = 7/2 or x = - 7/2 Not a choice

    A

    (x + 1) (4x - 11) = 0

    x = - 1 or

    x = 11/4

    A is not the answer
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