10th Class Mathematics Polynomials Question Bank Case Based (MCQs) - Polynomials

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    Case Study : Q. 11 to 15
    Applications   of   parabolas - highway   overpasses/ underpasses. A highway underpass is parabolic in shape.
    Parabola: A parabola is the graph that results from \[p(x)=a{{x}^{2}}+bx+c\] Parabolas are symmetric about a vertical line known as the axis of symmetry.
    Parabolic chamber \[y=2{{x}^{2}}/nw\]
    The axis of symmetry runs through the maximum or minimum point of the parabola which is called the vertex.
    Based on the above information, answer the following questions.
    If the highway overpass is represented by \[{{x}^{2}}-2x-8\].
    Then its zeroes are:

    A) \[(2,-4)\]

    B) \[(4,-2)\]

    C) \[(-2,-2)\]

    D) \[(-4,-4)\]

    Correct Answer: B

    Solution :

    [TRICK \[8=2\times 4=8\times 1\] \[\therefore \] Here, we will take 2 and 4 as a factors of 8. So, middle term becomes, \[-2=-4+2\] ]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}^{2}}-4x+2x-8\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,x(x-4)\,\,+2\,(x-4)\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,(x-4)\,\,(x+2)\]
    For zeroes.
                \[x-4=0\] or \[x+2=0\]
                \[x=4\] and \[-2\]
    So, option [b] is correct.

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