If b²-4ac = 0
If b²-4ac = 0, then the quadratic equation represented by the expression has one real root (solution)
If b²-4ac = 0, then the quadratic equation represented by the expression has one real root (solution). This condition is known as having a “discriminant” of 0.
To understand this further, let’s consider the general quadratic equation in the form: ax² + bx + c = 0, where a, b, and c are constants.
The discriminant, denoted by Δ, is given by the expression b²-4ac. It determines the nature of the roots of the quadratic equation.
When Δ = 0, it means that the quadratic equation has exactly one real root. This root is considered a “double root” or “repeated root” because it is the same value twice.
To find the value of the root, we can use the quadratic formula:
x = (-b ± √(b² – 4ac)) / (2a)
When Δ = 0, the quadratic formula becomes:
x = (-b ± √(0)) / (2a)
Simplifying this further, we have:
x = -b / (2a)
So, if b²-4ac = 0, the quadratic equation has one real root given by x = -b / (2a).
It is important to note that this root is only a real number, as the discriminant being 0 indicates that there are no imaginary or complex roots.
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