Understanding the Discriminant: When b²-4ac < 0, a Quadratic Equation Does Not Have Real Solutions

If b²-4ac < 0

If b²-4ac < 0, then the quadratic equation ax² + bx + c = 0 does not have real solutions

If b²-4ac < 0, then the quadratic equation ax² + bx + c = 0 does not have real solutions. Instead, it will have complex solutions. To understand why, we need to consider the discriminant, which is the expression b²-4ac. The discriminant helps us determine the nature of the solutions to a quadratic equation. When the discriminant is positive (b²-4ac > 0), the quadratic equation has two distinct real solutions.

When the discriminant is zero (b²-4ac = 0), the quadratic equation has one real solution.

However, when the discriminant is negative (b²-4ac < 0), the quadratic equation has no real solutions. Instead, it has two complex solutions. The complex solutions can be written in the form x = (-b ± √(b²-4ac))/(2a), where √(b²-4ac) represents the imaginary part of the solution. So, if b²-4ac < 0, the quadratic equation does not have real solutions but has two complex solutions.

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