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JEE Main & Advanced Sample Paper JEE Main Sample Paper-24

  • question_answer
    Number of distinct real solutions of the equation \[{{x}^{7}}+14{{x}^{5}}+16{{x}^{3}}+30-420=0\] is equal to

    A)  0                    

    B)  1

    C)  2                                

    D)  3

    Correct Answer: A

    Solution :

    Let \[f(x)={{x}^{7}}+14{{x}^{5}}+16{{x}^{3}}\,+30x-420\] \[\Rightarrow \,f'(x)\,=(7{{x}^{6}}\,+70{{x}^{4}}\,+48{{x}^{2}}+30)\,>0\forall x\in R\]\[\therefore \,\,f(x)\] is strictly increasing on R. So, the equation f(X) = 0 will have exactly one real root.


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