Which of the following is always true, Nature of Roots

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Solution

Q.
Which of the following is always true

1 One root of the equation $a x^{2} + b x + c = 0$ , in the form of $p + \sqrt{q}$ , then other root is $p - \sqrt{q}$ $(p \in z, q \in z^{+})$

2 If the equation $a x^{2} + b x + c = 0$ is satisfied by more than two distinct numbers (real or complex), then it becomes an identity.

3 If $a = 2$ and $b, c$ are integers and the roots of the quadratic equation $a x^{2} + b x + c = 0$ are rational, then the roots must be integers.

4 $a, b, c$ are in A.P and G.P then $(a, b, c)$ can be $(k, k, k)$ for all $k \in R$

Ans.
(2)

$a, b$ can be irrational

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