Discover the Mystery behind the Quadratic Equation with b²-4ac = 0 and Its One Real Solution

If b²-4ac = 0

1 real root

If b²-4ac = 0, then the quadratic equation ax²+bx+c=0 has only one real solution. To understand why, we need to use the quadratic formula which gives us the solutions of the equation as:

x = (-b ± √(b²-4ac))/2a

When b²-4ac = 0, then the square root term becomes √0 which is 0. Therefore, we get:

x = (-b ± 0)/2a

Simplifying further, we get:

x = -b/2a

This is the only real solution to the quadratic equation when b²-4ac = 0. Geometrically, this means that the graph of the quadratic equation is a perfect square with only one x-intercept. This happens when the vertex of the parabola, which is the lowest or highest point of the curve depending on the sign of a, is exactly on the x-axis.

It is important to note that if we are solving for x using the quadratic formula, we may still get two solutions even if b²-4ac = 0. This happens when the two solutions are complex conjugates of each other, where the square root term becomes imaginary. However, if we are only interested in real solutions, then b²-4ac = 0 implies only one real solution.

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