If b²-4ac < 0
If the expression b²-4ac is less than 0, it means that the discriminant of a quadratic equation is negative
If the expression b²-4ac is less than 0, it means that the discriminant of a quadratic equation is negative. The discriminant is the part of the quadratic formula (b²-4ac) that determines the nature of the solutions.
When the discriminant is negative, it implies that the quadratic equation does not have any real solutions. Instead, it has two complex solutions. Complex solutions consist of a real part and an imaginary part, involving the imaginary unit “i” (√-1).
To understand this better, let’s consider the quadratic formula:
x = (-b ± √(b²-4ac)) / (2a)
If b²-4ac < 0, the term under the square root, √(b²-4ac), will be imaginary. As a result, when we add or subtract this imaginary value from -b/(2a), we obtain complex solutions. Note that the rest of the formula remains the same. Therefore, for a quadratic equation with a negative discriminant, the solutions involve complex numbers.
More Answers:
Understanding the Product Rule in Calculus | Derivative of uv with Respect to xSimplified Quotient Rule | How to Find the Derivative of (u/v) with Respect to x
Understanding the Discriminant of Quadratic Equations | Nature and Solutions