Final answer:
The quadratic formula was applied to find the roots of the assumed correct form of the equation 2x² - 3400. Using the formula, it was found that the solutions are x = 41.25 and x = -41.25. However, these solutions do not match the provided answer choices, indicating a possible error in the given equation.
Step-by-step explanation:
To find the roots of the quadratic equation 2x² - 400 + 3000, you need to apply the quadratic formula. The equation should be in the standard form ax² + bx + c = 0. In this case, it looks like there might be a typo in the equation, as the constant term should typically be subtracted from the other terms. If we assume the equation should be 2x² - 400 - 3000 (which simplifies to 2x² - 3400), we can then identify that a = 2, b = 0, and c = -3400. The quadratic formula is x = (-b ± √(b²-4ac)) / (2a), which simplifies to x = ± √(-4ac) / (2a) because b = 0. Substituting the values of a and c into the formula, we get x = ± √(4*2*3400) / (2*2), which simplifies to x = ± √(27200) / 4. The square root of 27200 is 165, so the solutions are x = 165/4 and x = -165/4, which are x = 41.25 and x = -41.25, respectively. There appears to be a mismatch between the provided equation and the answer choices, as none of the choices match the calculated solutions. It's important to double-check the original equation for any errors before solving.