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

  • question_answer
    The number of zeroes that polynomial \[f(x)={{(x-2)}^{2}}+4\] can have is:

    A) 1

    B) 2

    C) 0

    D) 3

    Correct Answer: C

    Solution :

    \[f(x)={{(x-2)}^{2}}+4\]
    \[={{x}^{2}}+4-4x+4\]
    \[={{x}^{2}}-4x+8\]
    \[D={{b}^{2}}-4ac\]
    \[={{(-4)}^{2}}-4\times 1\times 8=16-32=-16\]      (1)
    \[D<0,\] so no real roots.
    So, option [c] is correct. 


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