To determine the value of the discriminant of a quadratic equation that has exactly one real number solution, we need to understand the role of the discriminant in the quadratic formula.
A quadratic equation is generally written in the form:
[tex]\[ ax^2 + bx + c = 0 \][/tex]
The discriminant ([tex]\(\Delta\)[/tex]) of a quadratic equation is given by:
[tex]\[ \Delta = b^2 - 4ac \][/tex]
The discriminant indicates the nature of the roots of the quadratic equation:
1. If [tex]\(\Delta > 0\)[/tex], the equation has two distinct real roots.
2. If [tex]\(\Delta = 0\)[/tex], the equation has exactly one real root.
3. If [tex]\(\Delta < 0\)[/tex], the equation has two complex roots.
Given that the quadratic equation has exactly one real number solution, we need to find the value of [tex]\(\Delta\)[/tex] that corresponds to this condition.
For the quadratic equation to have exactly one real number solution, the discriminant [tex]\(\Delta\)[/tex] must be equal to 0. This is because a discriminant of zero means the quadratic equation has a "double root" or "repeated root", which accounts for exactly one distinct real solution.
Therefore, the value of the discriminant for a quadratic equation that has exactly one real number solution is:
[tex]\[ \boxed{0} \][/tex]
