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10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

  • question_answer
    If \[\alpha \] and \[\beta \] are zeroes of the quadratic polynomial \[{{x}^{2}}-6x+a\]the value of 'a', if \[3\alpha +2\beta =20\]is -12

    A) True

    B) False

    C) Can't say

    D) Partially True/False

    Correct Answer: B

    Solution :

    False
    \[f\left( \alpha  \right)=f\left( \beta  \right)=0\]
    [\[\therefore \] \[\alpha \] and \[\beta \]are the zeroes of\[{{x}^{2}}-6x+a\]]
    \[{{\alpha }^{2}}-6\alpha +a=0\]
    \[{{\beta }^{2}}-6\beta +a=0\]
    \[\therefore \,\,\,\alpha +\beta =6\]                                           ...(i)
    \[3\alpha +2\beta =20\]                          [Given] ...(ii)
    From Eqs. (i) and (ii) we get \[\alpha =8\], \[\beta =-2\]
    \[{{\beta }^{2}}-6\beta +a=0\]
    \[a=6\times \left( -2 \right)-{{\left( -2 \right)}^{2}}\]
    \[=-12-4=-16\]


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