Question

what is the value of the discriminant, $b^{2}-4ac$, for the quadratic equation $0 = x^{2}-4x + 5$, 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: Identify coefficients

For the quadratic equation $0 = x^{2}-4x + 5$, we have $a = 1$, $b=-4$, $c = 5$.

Step2: Calculate discriminant

Substitute into $b^{2}-4ac$: $(-4)^{2}-4\times1\times5=16 - 20=-4$.

Step3: Determine number of real - solutions

If the discriminant $\Delta=b^{2}-4ac<0$, the quadratic equation has no real solutions. Since $\Delta=-4<0$, the equation has no real solutions.

Answer:

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