Do You Know About Roots?

Algebra Level 4

\(ax^2+bx+c=0\) is called a quadratic equation if \(a\neq 0\). Which of the following statements is/are true concerning quadratic equations?

\([1]\) A quadratic equation always has \(2\) distinct roots.

\([2]\) If \(a, b\) and \(c\) are all odd numbers, it is possible for \(ax^2+bx+c=0\) to have a rational solution.

\([3]\) If \(ax^2+bx+c=0\) has real solutions and \(a, b, c > 0\), then both solutions must be negative.

Note: This problem is a part of the set "I Don't Have a Good Name For This Yet". See the rest of the problems here. And when I say I don't have a good name for this yet, I mean it. If you like problems like these and have a cool name for this set, feel free to comment here.


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