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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Condition for common roots, Quadratic expressions and Position of roots

  • question_answer
    If \[{{x}^{2}}-hx-21=0,{{x}^{2}}-3hx+35=0\]\[(h>0)\]has a common root, then the value of \[h\] is equal to [EAMCET 1986]

    A) 1

    B) 2

    C) 3

    D) 4

    Correct Answer: D

    Solution :

    Subtracting, we get \[2hx=56\]or \[hx=28\] Putting in any, \[{{x}^{2}}=49\] \\[{{\left[ \frac{28}{h} \right]}^{2}}={{7}^{2}}\,\,\Rightarrow h=4(h>0)\]


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