Consider the statement that may have occurred to early algebraists:
A quadratic equation ax^2 +bx+c = 0 has a solution in the set of real
numbers if and only if its discriminant is non-negative, i.e., b^2-4ac=>0.
Is this statement true or false? If true, give a proof and explain what a proof of a mathematical statement is. If false, give a counterexample and explain what a counterexample
to a statement is.
I have no idea how to do this question please help.
ronaldo, a polynomial with two real roots implies that the discriminant is non-negative. However, a non-negative discriminant does not imply that the solutions are real. The proposition is then false. Plato gave the couterexample that proves this by contradiction:
but the solutions are not real.