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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 33

  • question_answer
    For all \['\,x\in R',\,\,{{x}^{2}}+2ax+ 10 -3a >0\], then the interval in which ?a? lies is

    A) \[a<-\,5\]          

    B)        \[-5<a<2\]

    C) \[a>5\]

    D)        \[2<a<5\]

    Correct Answer: B

    Solution :

    \[\operatorname{f}(x)= a{{x}^{2}}+ bx + c\] has same sign as that of a if \[\operatorname{D} < 0\]. \[{{\operatorname{x}}^{2}}+2ax+10-3a>O\forall x\] \[\Rightarrow \,\,\,\operatorname{D}\,<0\Rightarrow 4{{a}^{2}}-4(10-3a)<0\] \[\Rightarrow \,\,\,{{a}^{2}}+3a-10<0\] \[\Rightarrow \,\,\,\left( a+5 \right)\left( a\,-2 \right)<0\,\,\Rightarrow \,\,a\in \left( -\,5,\,\,2 \right)\]


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