When are these kinds of numbers solutions to quadratic equations?

Answer 1

You need to be more specific. A quadratic equation will have 2 solutions. The 2 solutions can be equal (such as x² + 2x + 1 = 0, solution is -1 and -1). If one of the solutions is a real number, then the other solution will also be a real number. If one of the solutions is a complex number, then the other solution will also be a complex number. [a complex number has a real component and an imaginary component]

In the equation: Ax² + Bx + C = 0. The term [B² - 4AC] will determine if the solution is a double-root, or if the answer is real or complex.

if B² = 4AC, then a double-root (real).

if B² > 4AC, then 2 real roots

if B² < 4AC, then the quadratic formula will produce a square root of a negative number, and the solution will be 2 complex numbers.

If B = 0, then the numbers will be either pure imaginary or real, and negatives of each other [ example 2i and -2i are solutions to x² + 4 = 0]

Example of 2 real and opposite sign: x² - 4 = 0; 2 and -2 are solutions.