Question

In the following question, two statements (i) and (ii) are given. Choose the valid statement.

1. The equation x² + x + 1 has two real roots.
2. Every quadratic equation can have at most two real roots.

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (ii)

Explanation:

Statement (i) is false because the discriminant of the equation x² + x + 1 = 0 is negative, so it has no real roots.
Statement (ii) is true since a quadratic equation is of degree 2 and can have at most two real roots.
Therefore, only statement (ii) is correct.