Question

Determine the discriminant for the quadratic equation 0 = -2x^2 + 13. Based on the discriminant value, how many real number solutions does the equation have?

A) 0
B) 1
C) 2
D) 24

Answer 1

The discriminant for the equation 0 = -2x^2 + 13, when calculated using the formula Δ = b^2 - 4ac, is 104. This positive value indicates that there are two distinct real number solutions to the quadratic equation.

Step-by-step explanation:

To determine the discriminant for the quadratic equation 0 = -2x^2 + 13, we rearrange it into the standard form of a quadratic equation, ax^2 + bx + c = 0. Here, a = -2, b = 0, and c = 13. The discriminant is given by the formula Δ = b^2 - 4ac.

Plugging in the values, we get:

Δ = (0)^2 - 4(-2)(13) = 0 + 104 = 104.

Since the discriminant is positive, this indicates that there are two distinct real number solutions to the quadratic equation. So, the answer to the question is C) 2.