Read the following information carefully and answer the questions given below.

2x² + 3x $$-$$ $$\alpha$$ = 0 has roots $$-$$2 and $$\beta$$ while the equation x² $$-$$ 3mx + 2m² = 0 has both roots positive, where $$\alpha$$ > 0 and $$\beta$$ > 0.

If $$\beta$$, 2, 2 m are in GP, then what is the value of $$\beta$$$$\sqrt m $$?

If c > 0 and 4a + c < 2b, then ax² $$-$$ bx + c = 0 has a root in which one of the following intervals?

Read the following information carefully and answer the questions given below.

Let $$\alpha$$ and $$\beta$$ ($$\alpha$$ < $$\beta$$) be the roots of the equation x² + bx + c = 0, where b > 0 and c < 0.

Consider the following

1. $$\beta$$ < $$-$$ $$\alpha$$

2. $$\beta$$ < | $$\alpha$$ |

Which of the above is/are correct?

Read the following information carefully and answer the questions given below.

Let $$\alpha$$ and $$\beta$$ ($$\alpha$$ < $$\beta$$) be the roots of the equation x² + bx + c = 0, where b > 0 and c < 0.

Consider the following

1. $$\alpha$$ + $$\beta$$ + $$\alpha$$$$\beta$$ > 0

2. $$\alpha$$²$$\beta$$ + $$\beta$$²$$\alpha$$ > 0

Which of the above is/are correct?