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BCECE Engineering BCECE Engineering Solved Paper-2014

  • question_answer
    The number of values of \[x\] in \[[0,2\pi ]\]satisfying  the equation \[3\text{ }\cos \text{ }2x-10\text{ }\cos \text{ }x\text{ }+\text{ }7\text{ }=\text{ }0\] is

    A) 1                                             

    B) 2      

    C) 3                                             

    D) 4

    Correct Answer: D

    Solution :

    Given, \[3\cos 2x-10\cos x+7=0\] \[\Rightarrow 3(2{{\cos }^{2}}x-1)-10\cos x+7=0\] \[\Rightarrow \]               \[6{{\cos }^{2}}x-10\cos x+4=0\] \[\Rightarrow \]               \[2[(3\cos x-2)(\cos x-1)]=0\] \[\Rightarrow \]               \[\cos x=1\] and \[\cos x=\frac{2}{3}\] Since, \[\cos x\]is positive in 1st and \[\text{IVth}\] quadrants. Hence, total number of solutions is 4.


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