# 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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