One root of $ax^2+bx+c=0$ in form $p+\sqrt{q}$, then other is $p-\sqrt{q}$
If $ax^2+bx+c=0$ is satisfied by more than two distinct numbers, it is an identity
If $a=2$, $b,c$ are integers and roots are rational, then roots must be integers
$a,b,c$ in AP and GP then $(a,b,c)=(k,k,k)$ for all $k\in\mathbb{R}$
Step-by-Step Solution
Key Concept: Analyze each: rational roots not necessarily integer; AP and GP constrain
Option 2 is always true (if degree-2 equation has $>2$ solutions, coefficients must all be 0, i.e., identity).
Correct Answer: 2