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the quadratic function a x^2 + b x + c = 0

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sanju09 GMAT Instructor
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the quadratic function a x^2 + b x + c = 0 Post Thu Apr 12, 2012 4:12 am
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    What is the sum of the rational numbers a, b, and c used in the quadratic function in variable x, a x^2 + b x + c = 0?
    I. The point (5 - √7, 0) lies on the graph of the quadratic function a x^2 + b x + c = 0.
    II. The point (5 + √7, 0) lies on the graph of the quadratic function a x^2 + b x + c = 0.



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    Post Thu Apr 12, 2012 4:48 am
    sanju09 wrote:
    What is the sum of the rational numbers a, b, and c used in the quadratic function in variable x, a x^2 + b x + c = 0?
    I. The point (5 - √7, 0) lies on the graph of the quadratic function a x^2 + b x + c = 0.
    II. The point (5 + √7, 0) lies on the graph of the quadratic function a x^2 + b x + c = 0.



    made up by Sanjeev K Saxena in the services of www.avenuesabroad.com
    One of the form of Quadratic equation is x^2 - Sum of the roots* x + Product of the roots.------(1)

    Stat. 1...

    As The point (5 - √7, 0) lies on the graph of the quadratic function a x^2 + b x + c = 0, hence one of the root is (5 - √7). This also implies that (5 + √7)is also a root.

    (5 + √7) is the conjugate of (5 - √7). So we know both roots.

    ...So sum of the roots = 5 + √7 + 5 - √7 = 10.
    Product of the roots = (5 - √7). (5 + √7)= 25 - 7 = 18.

    Putting these values in eqn 1.

    => x^2 - 10.x + 18 = 0.

    => or a = 1, b = -10, c =18. => a + b + c = 1 - 10 + 18 = 9.

    Stat. 1 is sufficient.

    Stat. 2...

    By similar logic, we can get a + b + c = 1 - 10 + 18 = 9.

    So Stat. 2 is also sufficient.

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    killer1387 GMAT Destroyer! Default Avatar
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    Post Fri Apr 13, 2012 3:39 am
    IMO D

    sanju09 GMAT Instructor
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    Post Sat Apr 14, 2012 12:49 am
    killer1387 wrote:
    IMO D
    nice opinion

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