If b²-4ac = 0
If b²-4ac = 0, it means that the discriminant of the quadratic equation is zero
If b²-4ac = 0, it means that the discriminant of the quadratic equation is zero. The discriminant is used to determine the nature of the solutions of a quadratic equation.
In general, the quadratic equation can be written as ax² + bx + c = 0, where a, b, and c are coefficients.
When the discriminant is zero, it indicates that the quadratic equation has only one real solution. This means that the quadratic equation has two identical solutions or roots. Mathematically, we can represent this as:
x = (-b ± √(b²-4ac)) / 2a
Since the discriminant is zero, it simplifies the equation to:
x = (-b ± √(0)) / 2a
= (-b ± 0) / 2a
= -b / 2a
Therefore, the quadratic equation with a discriminant of zero will have only one real solution given by x = -b/2a.
It’s important to note that when the discriminant is zero, the graph of the quadratic equation will touch the x-axis at only one point, which means it will have a single intersection with the x-axis.
I hope this explanation helps you understand the concept of a quadratic equation with a discriminant of zero. Let me know if you have any further questions!
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