An example of a quadratic equation with the given solutions ±3i√2 is x² + 18 = 0. This is derived by setting up the equation (x - 3i√2)(x + 3i√2) = 0 and then simplifying it.
The subject of the question is giving an example of a quadratic equation with the solutions ±3i√2. In Mathematics, especially in algebra, quadratic equations have the general form ax²+bx+c = 0.
Since ±3i√2 are complex conjugates, we can construct the quadratic equation by using the fact that if α and β are the roots of the quadratic equation, then the equation can be written as (x - α)(x - β) = 0.
An example of a quadratic equation with these solutions would be obtained by setting α = 3i√2 and β = -3i√2. Thus, the equation is (x - 3i√2)(x + 3i√2) = 0.
Expanding this, we get x² - (3i√2)² = 0, which simplifies to x² + 18 = 0 as the required quadratic equation.