Question

what is the value of the discriminant of the quadratic equation -2x²=-8x+8, and what does its value mean about the number of real number solutions the equation has?
the discriminant is equal to 0, which means the equation has no real number solutions.
the discriminant is equal to 0, which means the equation has one real number solution.
the discriminant is equal to 128, which means the equation has no real number solutions.
the discriminant is equal to 128, which means the equation has two real number solutions.

Explanation:

Step1: Escribir la ecuación en forma estándar

Dada la ecuación \( - 2x^{2}=-8x + 8\), sumamos \(8x - 8\) a ambos lados para obtener \( - 2x^{2}+8x - 8 = 0\). Multiplicando por \(-1\) (no afecta la discriminante), tenemos \(2x^{2}-8x + 8 = 0\). Aquí \(a = 2\), \(b=-8\) y \(c = 8\).

Step2: Calcular la discriminante

La fórmula de la discriminante para una ecuación cuadrática \(ax^{2}+bx + c = 0\) es \(D=b^{2}-4ac\). Sustituyendo los valores:

$$
LATEXBLOCK0
$$

Step3: Interpretar la discriminante

Si \(D = 0\), la ecuación cuadrática \(ax^{2}+bx + c = 0\) tiene una solución real (una raíz doble).

Answer:

The discriminant is equal to \(0\), which means the equation has one real number solution.