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

  • question_answer If the roots of the equation \[q{{x}^{2}}+px+q=0\]where p, q are real, be complex, then the roots of the equation \[{{x}^{2}}-4qx+{{p}^{2}}=0\] are

    A) Real and unequal

    B) Real and equal

    C) Imaginary

    D) None of these

    Correct Answer: A

    Solution :

    The given equations are          \[q{{x}^{2}}+px+q=0\] .....(i) and  \[{{x}^{2}}-4qx+{{p}^{2}}=0\] .....(ii) Roots of (i) are complex, therefore \[{{p}^{2}}-4{{q}^{2}}<0\] Now discriminant of (ii) is \[16{{q}^{2}}-4{{p}^{2}}=-4({{p}^{2}}-4{{q}^{2}})>0\] Hence, roots are real and unequal.

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