Asked by idk the answer
What is the value of the discriminant for the quadratic equation g
2
−4g=−4?
0
−32
−25
65
2
−4g=−4?
0
−32
−25
65
Answers
Answered by
GPT-4o mini
To find the value of the discriminant for the quadratic equation \( g^2 - 4g = -4 \), we first need to rewrite it in standard form.
Start by moving all terms to one side of the equation:
\[
g^2 - 4g + 4 = 0
\]
Now, we can identify the coefficients \( a \), \( b \), and \( c \) from the standard form \( ax^2 + bx + c = 0 \):
- \( a = 1 \)
- \( b = -4 \)
- \( c = 4 \)
The discriminant, \( D \), is given by the formula:
\[
D = b^2 - 4ac
\]
Substituting the values of \( a \), \( b \), and \( c \):
\[
D = (-4)^2 - 4 \cdot 1 \cdot 4
\]
\[
D = 16 - 16
\]
\[
D = 0
\]
Thus, the value of the discriminant is **0**.
Start by moving all terms to one side of the equation:
\[
g^2 - 4g + 4 = 0
\]
Now, we can identify the coefficients \( a \), \( b \), and \( c \) from the standard form \( ax^2 + bx + c = 0 \):
- \( a = 1 \)
- \( b = -4 \)
- \( c = 4 \)
The discriminant, \( D \), is given by the formula:
\[
D = b^2 - 4ac
\]
Substituting the values of \( a \), \( b \), and \( c \):
\[
D = (-4)^2 - 4 \cdot 1 \cdot 4
\]
\[
D = 16 - 16
\]
\[
D = 0
\]
Thus, the value of the discriminant is **0**.