11th Class Mathematics Conic Sections Question Bank Critical Thinking

  • question_answer
    The number of points of intersection of the two curves\[y=2\sin x\] and \[y=5{{x}^{2}}+2x+3\] is    [IIT 1994]

    A)            0     

    B)            1

    C)            2     

    D)            \[\infty \]

    Correct Answer: A

    Solution :

    Put \[y=2\sin x\]in \[y=5{{x}^{2}}+2x+3\]Þ\[2\sin x=5{{x}^{2}}+2x+3\] Þ \[5{{x}^{2}}+2x+3-2\sin x=0\]                               .....(i) \[x=\frac{-2\pm \sqrt{4-20(3-2\sin x)}}{10}\]. It is clear that number of intersection point is zero, because \[0\le \sin x\le 1\] and in all the values roots becomes imaginary.

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