Understanding Quadratic Equations: When b²-4ac = 0, find the Root

If b²-4ac = 0

If the quadratic equation b²-4ac = 0, then it means that the discriminant is equal to 0

If the quadratic equation b²-4ac = 0, then it means that the discriminant is equal to 0.

The discriminant, which is denoted by Delta (Δ), is calculated as Δ = b² – 4ac.

In this case, since Δ = 0, we can substitute it into the equation:

0 = b² – 4ac

Now, let’s solve this equation:

b² = 4ac

To find solutions for this equation, we need to consider different scenarios based on the discriminant value.

1. If Δ > 0, then there are two distinct real solutions for the quadratic equation.
2. If Δ = 0, then there is exactly one real solution, and the quadratic equation has a double root.
3. If Δ < 0, then there are no real solutions, and the quadratic equation has complex roots. Since we are given that Δ (b² - 4ac) = 0, it means that we are in the second scenario. For a quadratic equation b² - 4ac = 0 with a discriminant of 0, it will have a single real root. This equation with one root is also known as a perfect square trinomial.

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