JEE Main & Advanced Mathematics Quadratic Equations Question Bank Critical Thinking

  • question_answer 4) If the equations \[2{{x}^{2}}+3x+5\lambda =0\] and \[{{x}^{2}}+2x+3\lambda =0\] have a common root, then \[\lambda =\] [RPET 1989]

    A) 0

    B) -1

    C) \[0,-1\]

    D) 2,-1

    Correct Answer: C

    Solution :

    Given equations are \[2{{x}^{2}}+3x+5\lambda =0\] and \[{{x}^{2}}+2x+3\lambda =0\] have a common root if \[\frac{{{x}^{2}}}{-\lambda }=\frac{x}{-\lambda }=\frac{1}{1}\] Þ \[{{x}^{2}}=-\lambda ,x=-\lambda \]or \[\lambda =-1,\,\,0\].

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