Final answer:
The quadratic equation x^2 - 9x + 4 = 0 has two distinct real solutions, as the discriminant (b^2 - 4ac) is positive (65). Therefore, the correct answer is B) Two solutions.
Step-by-step explanation:
To determine the number of real solutions for the quadratic equation x^2 - 9x + 4 = 0, we can utilize the discriminant method from the quadratic formula, which is given by b^2 - 4ac, where the quadratic equation is of the form ax^2 + bx + c = 0. For this equation, a = 1, b = -9, and c = 4. Calculating the discriminant:
Discriminant = b^2 - 4ac
= (-9)^2 - 4(1)(4)
= 81 - 16
= 65
Because the discriminant is positive (65), there are two distinct real solutions for the given quadratic equation. So, the correct answer is B) Two solutions.