• # 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

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.