If b²-4ac < 0
When the value of b²-4ac is less than 0, it means that the quadratic equation ax² + bx + c = 0 has no real solutions
When the value of b²-4ac is less than 0, it means that the quadratic equation ax² + bx + c = 0 has no real solutions. This is because the discriminant, which is the value inside the square root in the quadratic formula, determines the nature of the solutions.
In this case, since b²-4ac < 0, the discriminant is negative. The quadratic formula is given by: x = (-b ± √(b²-4ac)) / (2a) When the discriminant is negative, it means that the square root of a negative number is involved, which results in complex solutions. Complex solutions involve the imaginary unit, usually denoted by the letter i, where i = √(-1). So, when b²-4ac < 0: 1. The quadratic equation ax² + bx + c = 0 has no real solutions. 2. The solutions will be complex numbers, in the form of x = (-b ± √(b²-4ac)i) / (2a). It's important to note that complex solutions come in conjugate pairs. For example, if one solution is a + bi, the other solution will be a - bi, where a and b are real numbers.
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