If a,b,c, a1,b1,c1 are rational and equa...

If `a,b,c, a_1,b_1,c_1` are rational and equations `ax^2+2bx+c=0 and a_1x^2+2b_1x+c_1=0` have one and only one root in common, prove that `b^2-ac and b_1^2-a_1c_1` must be perfect squares.

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