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

  • question_answer
    If the sum of the roots is \[-p\] and product of the roots \[-\frac{1}{p}\] is, then the quadratic polynomial is:

    A) \[k\left( -p{{x}^{2}}+\frac{x}{p}+1 \right)\]

    B) \[k\left( p{{x}^{2}}-\frac{x}{p}-1 \right)\]

    C) \[k\left( {{x}^{2}}+px-\frac{1}{p} \right)\]

    D) \[k\left( {{x}^{2}}-px+\frac{1}{p} \right)\]

    Correct Answer: C

    Solution :

    Given that, sum of the roots \[=-p\]
    and product of the roots \[=\frac{-1}{p}\]
    \[\therefore \]Required quadratic polynomial
    \[=k\,[{{x}^{2}}-(\text{sum of the roots})x+\text{product of the roots}]\] \[=k\left[ {{x}^{2}}-(-p)x+\left( -\frac{1}{p} \right) \right]=k\left[ {{x}^{2}}+px-\frac{1}{p} \right]\]
    where k is an arbitrary constant.                         
    So, option [c] is correct.

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