Final answer:
None of the provided options (A, B, C, D) are correct. The actual solutions to the equation 2x^2 + 9x + 4 = 0, found using the quadratic formula, are x = -0.5 and x = -4.
Step-by-step explanation:
To find the solutions to the quadratic equation 2x^2 + 9x + 4 = 0, we can use the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / (2a). For this equation, a = 2, b = 9, and c = 4.
We first compute the discriminant (b^2 - 4ac): (9)^2 - 4(2)(4) = 81 - 32 = 49.
Since the discriminant is positive, there are two real solutions which we can find by substituting the values of a, b, and c into the quadratic formula:
- x = (-9 + √49) / (2 * 2) = (-9 + 7) / 4 = -0.5
- x = (-9 - √49) / (2 * 2) = (-9 - 7) / 4 = -4
Thus, none of the solutions provided (A. x = 2, B. x = -3, C. x = 7, D. x = 4) are correct. The actual solutions to the equation 2x^2 + 9x + 4 = 0 are x = -0.5 and x = -4.