Kenneth Rosen Edition 6th Exercise 1.4 Question 44 (Page No. 62)

Question

Use quantifiers and logical connectives to express the fact that a quadratic polynomial with real number coefficients has at most two real roots.

answer I think is

∀a∀b∀c[∃x ∃y ((ax2+ bx+c=0 )∨ (ay2+ by+c=0)) ∧ (∀w(aw2+ bw+c=0) $\rightarrow$ (w=x ∨ w=y)]

Comments

∀a∀b∀c[∃x ∃y ((ax²+ bx+c=0 ) $\wedge$ (ay²+ by+c=0)) ∧ (∀w(aw²+ bw+c=0) -> (w=x ∨ w=y)]

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Yaa that first 'or' should be 'and'.  Remaining portion is right??

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This will be always false, since there are quadratic equations for which there is no real solution or only one solution.

For example, 2x^2 + 2X +1=0 has no real solution, hence if we put a=2,b=2,c=1 then, the entire expression inside will be false, and we know that in a case of universal quantifier(∀) even if one assignment is false then, the entire proposition will be false.

Correct solution I guess:http://www.slader.com/textbook/9780073383095-discrete-mathematics-with-applications-7th-edition/68/exercises/44/