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

  • question_answer
    If \[p(x)=a{{x}^{2}}+bx+c\] and \[a+b+c=0,\] then one zero is:

    A) \[\frac{-b}{a}\] 

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

    C) \[\frac{b}{c}\]

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

    Correct Answer: B

    Solution :

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

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