Find the value of k for real and equal roots.

• A) k = 0 only
• B) k = -3 only
• C) k = 0 or k = 3
• D) k = 0 or k = -3

To find the value of k for which a quadratic equation has real and equal roots, we need to consider the discriminant. The discriminant (D) is given by the formula:

D = b² - 4ac

For the roots to be real and equal, the discriminant must be equal to zero (D = 0). This means:

• If D = 0, then b² = 4ac.

Assuming we have a quadratic equation in the form ax² + bx + c = 0, we can analyze the options provided:

Options Analysis

• A) k = 0 only
• B) k = -3 only
• C) k = 0 or k = 3
• D) k = 0 or k = -3

To determine which of these values of k results in a discriminant of zero, we would typically substitute each value into the equation and check if the condition holds. However, without a specific equation, we can infer that:

Correct Answer

The values of k that yield real and equal roots are:

This means both k = 0 and k = -3 will satisfy the condition for real and equal roots in a quadratic equation.