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

  • question_answer
    Case Study : Q. 31 to 35
    A group of school friends went on an expedition to see caves. One person remarked that the entrance of the caves resembles a parabola, and can be represented by a quadratic polynomial \[f(x)=a{{x}^{2}}+bx+c,\] \[a\ne 0,\] where a, b and c are real numbers.
    Based on the above information give the answer of the following questions.
    If one of the zeroes of the quadratic polynomial \[(p-1){{x}^{2}}+px+1\]is 4, then the value of p is:

    A) \[\frac{3}{5}\]

    B) \[\frac{3}{4}\]

    C) \[\frac{2}{5}\]

    D) \[\frac{1}{5}\]

    Correct Answer: B

    Solution :

    Since, \[x=4\]is one of the zero of the polynomial \[(p-1){{x}^{2}}+px+1\]then
                \[\Rightarrow \,\,\,\,\,\,\,\,\,16p-16+4p+1=0\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,20p=15\Rightarrow p=\frac{3}{4}\]
    So, option [b] is correct.

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