10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

  • question_answer
    If sum of the squares of zeroes of the quadratic polynomial \[f\left( x \right)={{x}^{2}}-4x+k\]is 20, then the value of k is

    A) -2

    B) -3

    C) -4

    D) 2

    Correct Answer: A

    Solution :

    Let \[\alpha \] and \[\beta \]be the zeroes of\[f\left( x \right)\].
    Given, \[{{\alpha }^{2}}+{{\beta }^{2}}=20\]
    \[{{\left( \alpha +\beta  \right)}^{2}}-2\alpha \beta =20\]                ...(i)
    For the equation, \[f\left( x \right)={{x}^{2}}-4x+k\]
    \[\alpha +\beta =4\]
    \[\alpha \beta =k\]
    Put these values in Eq. (i)
    \[\Rightarrow \,\,\,{{\left( 4 \right)}^{2}}-2k=20\]
    \[\Rightarrow \,\,16-2k=20\]
    \[\Rightarrow \,\,\,2k=-4\]
    \[\Rightarrow \,\,k=-2\]


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