A tough problem for me , need help!

If each pair of 3 equations $ x^2+p_1x+q_1=0 $,$ x^2+p_2x+q_2=0 $&$ x^2+p_3x+q_3=0 $ have a common root , then prove that $ p_1 ^2+ p_2 ^2+p_3 ^2+4(q_1+q_2+q_3)=2(p_1p_2+p_2p_3+p_3p_1) $

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