The discriminant of a quadratic polynomial is a key factor in determining the nature of its roots. The discriminant, denoted as D, is calculated as the expression b² - 4ac, where a, b, and c are the coefficients of the quadratic polynomial in the standard form ax² + bx + c.

When the discriminant is greater than zero (D > 0), it implies that the quadratic polynomial has two real and unequal roots. This can be explained in detail as follows:

1. Definition of Discriminant:
The discriminant is a mathematical term used to determine the nature of the roots of a quadratic polynomial. It is calculated using the formula D = b² - 4ac, where a, b, and c are the coefficients of the quadratic polynomial.

2. Nature of Discriminant:
The discriminant can take three different values:

- If the discriminant is greater than zero (D > 0), it means that the quadratic polynomial has two real and unequal roots.
- If the discriminant is equal to zero (D = 0), it means that the quadratic polynomial has two real and equal roots.
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3. Explanation of Option B:
In the given question, the discriminant is stated to be greater than zero (D > 0). According to the nature of the discriminant, this implies that the quadratic polynomial has two real and unequal roots. Therefore, the correct answer is option B.

4. Example:
Consider the quadratic polynomial x² - 5x + 6. To determine the nature of its roots, we can calculate the discriminant using the formula D = b² - 4ac. Here, a = 1, b = -5, and c = 6.

D = (-5)² - 4(1)(6) = 25 - 24 = 1

Since the discriminant (D = 1) is greater than zero, the quadratic polynomial has two real and unequal roots.

By considering the nature of the discriminant, we can conclude that when the discriminant is greater than zero (D > 0), the quadratic polynomial has two real and unequal roots.