Let p,q,r be positive real numbers, not all equal, such that some two of the equations \begin{eqnarray*} px^2 + 2qx + r &=& 0 \\ qx^2 + 2rx + p &=& 0 \\ rx^2 + 2px + q &=& 0 . \\ \end{eqnarray*} have a common root, say α. Prove that a) α is real and negative;b) the remaining third quadratic equation has non-real roots. quadraticsVietaalgebraalgebra unsolved