Can there be a real and imaginary solution to a quadratic equation?

Answer 1

Yes, there can be a pure imaginary imaginary solution, as i2 =-1 and -i2 = 1. Or there can be a pure real solution or there can be a complex solution.

For a quadratic equation ax2+ bx + c = 0, it depends on the value of the discriminant [b2 - 4ac], which is the value inside the radical of the quadratic formula.

• [b2 - 4ac] > 0 : Two distinct real solutions.
• [b2 - 4ac] = 0 : Two equal real solutions (double root).
• [b2 - 4ac] < 0 : Two complex solutions; they will be pure imaginary if b = 0, they will have both real and imaginary parts if b is nonzero.