Here is the solution which contents quantifiers and logical connectives that express <span> the fact that a quadratic polynomial with real number coefficients has at most two real roots and I am pretty sure you will find it helpful :
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∀a<span>∀b∀c[∃x ∃y ((ax2+ bx+c=0 )∨ (ay</span>2+ by+c=0)) ∧ (∀w(aw2<span>+ bw+c=0) <span>→→</span> (w=x ∨ w=y)]
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Hope you will agree with me.
Regards!
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