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JEE Main & Advanced Sample Paper JEE Main Sample Paper-23

  • question_answer
    Let \[f(x)=({{a}^{2}}+a+2){{x}^{2}}-(a+4)x-7,x\in R\]. If unity lies between the roots of equation \[f(x)=0\] then number of integral values of a is

    A)  5                                

    B)  4

    C)  3                                

    D)  2

    Correct Answer: A

    Solution :

    Coefficient of \[{{x}^{2}}>0\] (always) \[\Rightarrow \,f(1)<0\] \[\Rightarrow ({{a}^{2}}+a+2)\,-a-4-7<0\] \[\Rightarrow \,{{a}^{2}}-9<0\Rightarrow \,3<a<3\] \[\Rightarrow \] Number of integral values of a is 5 i.e., \[\{-2,\,-1,\,\,0,\,1,\,2\}\].


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