Question

what is the value of the discriminant, ( b^{2}-4 a c ), for the quadratic equation ( 0=x^{2}-4 x + 5 ), and what does it mean about the number of real solutions the equation has?
the discriminant is -4, so the equation has 2 real solutions.
the discriminant is -4, so the equation has no real solutions.
the discriminant is 35, so the equation has 2 real solutions.
the discriminant is 35, so the equation has no real solutions.

Explanation:

Step1: Identificar los valores de \(a\), \(b\) y \(c\)

Para la ecuación \(x^{2}-4x + 5=0\), \(a = 1\), \(b=-4\), \(c = 5\).

Step2: Calcular el discriminante

Usamos la fórmula \(b^{2}-4ac\). Sustituimos los valores: \((-4)^{2}-4\times1\times5=16 - 20=-4\).

Step3: Interpretar el discriminante

Si el discriminante \(D=b^{2}-4ac<0\), la ecuación cuadrática \(ax^{2}+bx + c = 0\) no tiene soluciones reales.

Answer:

The discriminant is \(-4\), so the equation has no real solutions.