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

  • question_answer
    A quadratic polynomial whose one zero is \[-3\] and product of zeroes is 0, is:

    A) \[3{{x}^{2}}+3\]

    B) \[{{x}^{2}}-3x\]

    C) \[{{x}^{2}}+3x\]

    D) \[3{{x}^{2}}-3\]

    Correct Answer: C

    Solution :

    Let \[\alpha \] and \[\beta \] be the zeroes of the required polynomial.
    Given,    \[\alpha =-3\]and \[\alpha \cdot \beta =0\]
    \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,-3\cdot \beta =0\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\beta =0\]
    Now, required polynomial
                            \[={{x}^{2}}-(\alpha +\beta )x+\alpha \beta \]
    So, option [c] is correct.

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