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

  • question_answer
    If \[p(x)=a{{x}^{2}}+bx+c\] and \[a+c=b,\] then one of the zeroes is:

    A) \[\frac{b}{a}\]

    B) \[\frac{c}{a}\]

    C) \[\frac{-c}{a}\]

    D) \[\frac{-b}{a}\]

    Correct Answer: C

    Solution :

    Take  \[x=-1\]
    \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,p(-1)=a{{(-1)}^{2}}+b(-1)+c=a-b+c=b-b=0\]                                            \[[a+c=b]\]
    \[\therefore \] one zero \[(\alpha )=1\]
    \[\alpha \beta =\]product of zeroes \[=\frac{c}{a}\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,(-1)\cdot \beta =\frac{c}{a}\Rightarrow \beta =-\frac{c}{a}\]
    So, option [c] is correct.

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