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JEE Main & Advanced Sample Paper JEE Main Sample Paper-34

  • question_answer
    The total number of polynomials of the form\[{{x}^{3}}+a{{x}^{2}}+bx+c\] that are divisible by \[{{x}^{2}}+1\], where \[a,b,c\text{ }\in \text{ }\left\{ 1,2,3..........9,10 \right\}\]is equal to

    A)  5                                            

    B)  8

    C)  10                                         

    D)  15

    Correct Answer: C

    Solution :

    We must have, \[{{i}^{3}}+a{{i}^{2}}+bi+c=0\] and             \[{{(-i)}^{3}}+a{{(-i)}^{2}}+b(-i)+c=0\]             \[\Rightarrow \,(c-a)+i(b-1)=0\]             \[\Rightarrow \,b=1;\,\,\,c=a\] \[\therefore \] Total number of polynomials \[{{=}^{10}}{{C}_{1}}=10\]


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