## If b²-4ac < 0

### The expression b² – 4ac is called the discriminant

The expression b² – 4ac is called the discriminant. It is often used to determine the nature of the solutions of a quadratic equation. Specifically, if b² – 4ac is less than zero (b² – 4ac < 0), it means that the quadratic equation does not have any real solutions. To understand why this is the case, let's consider the quadratic equation in its standard form: ax² + bx + c = 0, where a, b, and c are constants. The discriminant, denoted as Δ, is given by Δ = b² - 4ac. It acts as a determinant to determine the nature of the solutions. When Δ is less than zero, it means that the quadratic equation does not intersect the x-axis. In other words, the equation does not have any real solutions. Instead, it has two complex solutions, which are in the form of a+bi and a-bi, where a and b are real numbers, and i is the imaginary unit (√(-1)). These complex solutions occur when the quadratic equation has complex roots that lie on the complex plane rather than on the real number line. In summary, if b² - 4ac is less than zero, it implies that the quadratic equation does not have any real solutions and instead has complex solutions.

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Understanding Quadratic Equations | The Significance of b²-4ac > 0