10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

  • question_answer
    If \[\alpha \] and \[\beta \]are the zeroes of the quadratic polynomial \[f\left( x \right)={{x}^{2}}-4x+3\], then the value of\[{{\alpha }^{4}}{{\beta }^{3}}+{{\alpha }^{3}}{{\beta }^{4}}\] is

    A) 104

    B) 108

    C) 112

    D) 5

    Correct Answer: B

    Solution :

    \[\alpha\]  and  \[\beta\]are the zeroes of  \[f\left( x \right)={{x}^{2}}-4x+3\]
     We know that,
                            \[\alpha +\beta =-\frac{b}{a}=4\]
     and                 \[\alpha \,.\,\beta =\frac{c}{a}=3\]
     \[\Rightarrow \,\,\,{{\alpha }^{4}}{{\beta }^{3}}+{{\alpha }^{3}}{{\beta }^{4}}={{\alpha }^{3}}{{\beta }^{3}}\left( \alpha +\beta  \right)\]
     \[\Rightarrow \,\,{{\left( \alpha \,\beta  \right)}^{3}}\left( \alpha +\beta  \right)={{\left( 3 \right)}^{3}}\left( 4 \right)\]
                            \[=4\times 27=108\]


You need to login to perform this action.
You will be redirected in 3 sec spinner