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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Solution of quadratic equations and Nature of roots

  • question_answer
    If \[\sin A,\sin B,\cos A\] are in G.P., then roots of \[{{x}^{2}}+2x\cot B+1=0\] are always [Orissa JEE 2005]

    A) Real

    B) Imaginary

    C) Greater than 1

    D) Equal

    Correct Answer: A

    Solution :

    Given \[{{\sin }^{2}}B=\sin A\cos A\] Þ \[\cos 2B=1-\sin 2A\ge 0\] Now for \[{{x}^{2}}+2x\cot B+1=0\] Consider \[D=4({{\cot }^{2}}B-1)=4\cos 2B\cos \text{e}{{\text{c}}^{\text{2}}}B\ge 0\] Hence, roots are always real.


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