## If b²-4ac < 0

### If b²-4ac is less than 0, it means that the discriminant is negative

If b²-4ac is less than 0, it means that the discriminant is negative. The discriminant is the part of the quadratic formula that is inside the square root, given by b²-4ac.

A negative discriminant indicates that the quadratic equation does not have any real solutions. In other words, the quadratic equation does not intersect or touch the x-axis.

When solving a quadratic equation using the quadratic formula: x = (-b ± √(b²-4ac))/(2a), the square root part (√(b²-4ac)) will result in imaginary numbers.

For example, if we have the quadratic equation 3x² + 2x + 1 = 0 and calculate the discriminant, b²-4ac, we get 2² – 4(3)(1) = 4 – 12 = -8, which is negative.

Therefore, the equation 3x² + 2x + 1 = 0 does not have any real solutions. The solutions will involve the imaginary unit “i” and will be in the form of complex numbers.

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