An example of a quadratic equation with the given solutions ±3i√2 is x² + 18 = 0, derived by setting up the equation as (x - 3i√2)(x + 3i√2) = 0 and simplifying it.
The question deals with finding a quadratic equation given the solutions ±3i√2. We know that if α and β are the solutions of the quadratic equation ax² + bx + c = 0, then the equation can be written as (x - α)(x - β) = 0.
In this case, the solutions are ±3i√2, which means the equation can be constructed as (x - 3i√2)(x + 3i√2) = 0.
To simplify, we utilize the difference of squares formula: (x² - (3i√2)²) = x² - (3² ⋅ (i²) ⋅ (√2)²) = x² - (-9 ⋅ 2) = x² + 18 = 0.
Therefore, an example of a quadratic equation with the given solutions ±3i√2 is x² + 18 = 0.