Question
What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = x2 − 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.
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.
Answers
GPT-4o mini
To find the value of the discriminant for the quadratic equation \( 0 = x^2 - 4x + 5 \), we use the formula for the discriminant, given by:
\[
D = b^2 - 4ac
\]
In the equation \( x^2 - 4x + 5 \):
- \( a = 1 \)
- \( b = -4 \)
- \( c = 5 \)
Now, we can calculate the discriminant:
\[
D = (-4)^2 - 4(1)(5)
\]
\[
D = 16 - 20
\]
\[
D = -4
\]
Since the discriminant \( D \) is negative (\( -4 \)), this indicates that the quadratic equation has no real solutions.
Therefore, the correct statement is: **The discriminant is −4, so the equation has no real solutions.**
\[
D = b^2 - 4ac
\]
In the equation \( x^2 - 4x + 5 \):
- \( a = 1 \)
- \( b = -4 \)
- \( c = 5 \)
Now, we can calculate the discriminant:
\[
D = (-4)^2 - 4(1)(5)
\]
\[
D = 16 - 20
\]
\[
D = -4
\]
Since the discriminant \( D \) is negative (\( -4 \)), this indicates that the quadratic equation has no real solutions.
Therefore, the correct statement is: **The discriminant is −4, so the equation has no real solutions.**