Do You Know About Roots?

Algebra Level 4

ax2+bx+c=0ax^2+bx+c=0 is called a quadratic equation if a0a\neq 0. Which of the following statements is/are true concerning quadratic equations?

[1][1] A quadratic equation always has 22 distinct roots.

[2][2] If a,ba, b and cc are all odd numbers, it is possible for ax2+bx+c=0ax^2+bx+c=0 to have a rational solution.

[3][3] If ax2+bx+c=0ax^2+bx+c=0 has real solutions and a,b,c>0a, 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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