## If b²-4ac = 0

### The equation b²-4ac = 0 is called the discriminant of a quadratic equation

The equation b²-4ac = 0 is called the discriminant of a quadratic equation. In quadratic equations of the form ax² + bx + c = 0, the discriminant helps us determine the nature of the roots (solutions) of the equation.

Here’s what you can infer from the discriminant value:

1. If the discriminant is positive (b²-4ac > 0), then the quadratic equation has two distinct real roots. This means that when you solve the equation, you will find two different values for x that satisfy the equation.

2. If the discriminant is zero (b²-4ac = 0), then the quadratic equation has one real root. This means that when you solve the equation, you will find only one value for x that satisfies the equation. Moreover, this root will be a double root or a repeated root because the quadratic equation touches or intersects the x-axis at exactly one point.

3. If the discriminant is negative (b²-4ac < 0), then the quadratic equation has no real solutions. This means that there are no values of x that satisfy the equation within the real number system. In this case, the roots of the quadratic equation will be complex or imaginary numbers. To solve a quadratic equation and find its roots, you can use the quadratic formula: x = (-b ± √(b²-4ac))/(2a) To summarize, if the discriminant of a quadratic equation is zero, the equation has one real root, and if the discriminant is positive, the equation has two distinct real roots. However, if the discriminant is negative, the equation has no real solutions.

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