Question
Find the discriminant.
z^2 - 5z + 5 = 0
z^2 - 5z + 5 = 0
Answers
GPT-4o mini
To find the discriminant of the quadratic equation \( z^2 - 5z + 5 = 0 \), we can use the formula for the discriminant:
\[
D = b^2 - 4ac
\]
where \( a \), \( b \), and \( c \) are the coefficients from the quadratic equation in the standard form \( az^2 + bz + c = 0 \).
In this case, we have:
- \( a = 1 \)
- \( b = -5 \)
- \( c = 5 \)
Now, we can substitute these values into the discriminant formula:
\[
D = (-5)^2 - 4 \cdot 1 \cdot 5
\]
Calculating each part:
\[
D = 25 - 20
\]
\[
D = 5
\]
Thus, the discriminant of the equation \( z^2 - 5z + 5 = 0 \) is \( \boxed{5} \).
\[
D = b^2 - 4ac
\]
where \( a \), \( b \), and \( c \) are the coefficients from the quadratic equation in the standard form \( az^2 + bz + c = 0 \).
In this case, we have:
- \( a = 1 \)
- \( b = -5 \)
- \( c = 5 \)
Now, we can substitute these values into the discriminant formula:
\[
D = (-5)^2 - 4 \cdot 1 \cdot 5
\]
Calculating each part:
\[
D = 25 - 20
\]
\[
D = 5
\]
Thus, the discriminant of the equation \( z^2 - 5z + 5 = 0 \) is \( \boxed{5} \).