If the discriminant is 0,
then it has one solution, real number, double root
If the discriminant of a quadratic equation is 0, it means that the quadratic equation has exactly one real root or solution. This occurs when the discriminant, which is the term under the square root in the quadratic formula, equals zero. Specifically, for a quadratic equation of the form ax^2 + bx + c = 0, the discriminant is given by b^2 – 4ac.
When the discriminant is 0, the quadratic equation has only one solution that is a real number. This is referred to as a double root or a repeated root. Geometrically, this means that the quadratic function represented by the equation has a vertex that is located on the x-axis, which is where the single solution is found.
From a practical standpoint, this means that if you are trying to solve a quadratic equation with a discriminant of 0, you can use the quadratic formula to find the single solution. Additionally, you can use this information to determine the nature of the roots of the quadratic equation, as well as the shape of the graph of the quadratic function.
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