If b²-4ac = 0
1 real root
If b²-4ac = 0, it means that the discriminant of a quadratic equation is zero. The discriminant is the expression inside the square root in the quadratic formula (x = (-b±sqrt(b²-4ac))/2a). The value of the discriminant determines the nature of the roots of the quadratic equation.
When the discriminant is zero, it means that the quadratic equation has only one real root. This is because the quadratic formula involves taking the square root of the discriminant, and when the discriminant is zero, we have √0 = 0, so the formula gives x = -b/2a, which is the formula for the vertex of the parabola.
So, if b²-4ac = 0, the quadratic equation has one real root, and it is a perfect square. This means that the quadratic can be factored into (x – r)² = 0, where r is the real root of the quadratic.
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