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9th Class Mathematics Polynomials Question Bank Polynomials

  • question_answer
    If polynomials \[\mathbf{2}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+a}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+3x-5}\] and \[{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-2x+a}\] are divided by\[\left( \mathbf{x-2} \right)\], the same remainders are obtained. Find the value of a.

    A)  -3    

    B)  3             

    C)  -4                               

    D)  -9

    Correct Answer: A

    Solution :

    (a):\[f{{(x)}^{2}}=2{{x}^{3}}+a{{x}^{2}}+3x-5;\] \[g(x)={{x}^{3}}+{{x}^{2}}~-2x+a\] By Remainder Theorem, \[f\left( 2 \right)=\left( 2\times {{2}^{3}}+a\times {{2}^{2}}+3\times 2-5 \right)=17+4a\] Again, \[g(2)=\left( {{2}^{3}}+{{2}^{2}}-2\times 2+a \right)=8\therefore 17+4a=8+a\]\[\Rightarrow 3a=-9\Rightarrow a=-3\]                          


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