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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