determine the nature of the solutions of the equation, one real solution, two real solutions, or two non-real solutions. x^2-20x+100=0
B^2 = 400, 4AC = 400, sqrt(400-400)= 0
Since the value under the radical = 0,
There iS 1 real solution.
To determine the nature of the solutions of the equation x^2 - 20x + 100 = 0, we can use the discriminant.
The discriminant (Δ) of a quadratic equation of the form ax^2 + bx + c = 0 is given by the formula Δ = b^2 - 4ac.
In this case, the coefficient of x^2 is a = 1, the coefficient of x is b = -20, and the constant term is c = 100. Plugging these values into the discriminant formula, we get:
Δ = (-20)^2 - 4 * 1 * 100
= 400 - 400
= 0
The nature of the solutions depends on the value of the discriminant (Δ):
1. If Δ > 0, there are two distinct real solutions.
2. If Δ = 0, there is exactly one real solution.
3. If Δ < 0, there are two non-real solutions (complex conjugates).
In this case, since Δ = 0, we conclude that the equation x^2 - 20x + 100 = 0 has exactly one real solution.