Question

How many solutions does the quadratic y=−x2+4x−5 have?(1 point)
Responses

Two real number solutions
Two real number solutions

One real number solution
One real number solution

No real number solutions
No real number solutions

Answer 1

To determine the number of solutions for the quadratic equation \( y = -x^2 + 4x - 5 \), we need to analyze it by using the discriminant method. The general form of a quadratic equation is \( ax^2 + bx + c = 0 \), where:

- \( a = -1 \)
- \( b = 4 \)
- \( c = -5 \)

The discriminant \( D \) is calculated using the formula:

\[
D = b^2 - 4ac
\]

Substituting the values:

\[
D = 4^2 - 4 \cdot (-1) \cdot (-5) = 16 - 20 = -4
\]

Since the discriminant \( D \) is negative (\( D = -4 \)), this indicates that there are no real number solutions to the quadratic equation.

Therefore, the answer is:

**No real number solutions**.