If b²-4ac < 0
There are no roots
If b²-4ac < 0, then the quadratic equation ax² + bx + c = 0 has no real solutions. This is because the value of the discriminant (b²-4ac) indicates the nature of the solutions of the quadratic equation. If the discriminant is less than zero, it means that the quadratic has no real roots. This occurs when the graph of the quadratic equation does not intersect the x-axis at any point, which happens when the discriminant is negative. For example, consider the quadratic equation x² + 2x + 3 = 0. Here, a=1, b=2 and c=3. The discriminant is b²-4ac = 2²-4(1)(3) = -8, which is negative. Therefore, the equation has no real solutions. However, it is important to note that the quadratic equation may still have complex solutions involving imaginary numbers. In this case, the solutions are in the form of complex conjugates (a+bi and a-bi), where i is the imaginary unit.
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