If b²-4ac < 0
There are no roots
If b²-4ac < 0, it means that the discriminant, which is the expression under the square root symbol in the quadratic formula, is negative. This indicates that the quadratic equation does not have any real solutions, and instead has two complex conjugate solutions. To find the solutions of a quadratic equation when the discriminant is negative, we can use the quadratic formula: x = (-b ± √(b²-4ac)) / 2a Since the discriminant is negative, the square root term will be imaginary. We can simplify the expression by factoring out -1 from the radical: x = (-b ± i√(4ac-b²)) / 2a where i represents the square root of -1. This gives us two complex conjugate solutions: x = (-b + i√(4ac-b²)) / 2a and x = (-b - i√(4ac-b²)) / 2a These solutions are usually written in the form of a complex number, a + bi, where a and b are real numbers and i represents the square root of -1.
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