11th Class Mathematics Complex Numbers and Quadratic Equations Question Bank Critical Thinking

  • question_answer For the equation \[3{{x}^{2}}+px+3=0,\,p>0\] if one of the root is square of the other, then p is equal to  [IIT Screening 2000]

    A) \[\frac{1}{3}\]

    B) 1

    C) 3

    D) \[\frac{2}{3}\]

    Correct Answer: C

    Solution :

    \[\alpha +{{\alpha }^{2}}=-\frac{p}{3}\] and \[\alpha .{{\alpha }^{2}}=1.\] So\[\alpha =1,\]\[\omega ,\,{{\omega }^{2}}\]. If \[\alpha =1,p<0\]. If \[\alpha =\omega \,\,\text{or}\,\,{{\omega }^{2}},\] we have \[\omega +{{\omega }^{2}}=-\frac{p}{3}\,\] Þ  \[-1=\frac{-p}{3}\,\,\,\,\,\Rightarrow \,\,p=3\].

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