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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
    For what value of k will the equation\[{{x}^{2}}-(3k-1)x+\]\[2{{k}^{2}}+2k\] have equal roots  [Karnataka CET 1998]

    A) 5

    B) 9

    C) Both (a) and (b)

    D) 0

    Correct Answer: C

    Solution :

    For the equation to be real roots, \[{{b}^{2}}-4ac=0\] Þ \[{{(3k-1)}^{2}}=4(2{{k}^{2}}+2k-11)\] Þ \[9{{k}^{2}}+1-6k=8{{k}^{2}}+8k-44\] Þ \[{{k}^{2}}-14k+45=0\] Þ \[(k-5)(k-9)\] = 0 \[k=5\]or\[k=9\].


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