If b²-4ac = 0
If the expression b²-4ac equals zero, then it means that the quadratic equation associated with this expression has exactly one real root
If the expression b²-4ac equals zero, then it means that the quadratic equation associated with this expression has exactly one real root. The quadratic equation is usually written in the form ax²+bx+c = 0, where a, b, and c are constants.
To understand this better, let’s examine the quadratic formula. The quadratic formula provides a way to find the roots of a quadratic equation: x = (-b ± √(b²-4ac))/(2a). In this formula, the expression inside the square root, b²-4ac, is called the discriminant.
When the discriminant is zero, it means that the square root term in the quadratic formula simplifies to zero. So, the formula becomes x = (-b ± 0)/(2a), which simplifies to x = -b/(2a). Therefore, the equation has a single real root, and that root is -b/(2a).
It’s important to note that when the discriminant is positive, there are two distinct real roots. When the discriminant is negative, there are no real roots, only complex roots.
In summary, if the expression b²-4ac equals zero, it indicates that the quadratic equation has one real root.
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