Asked by idk the answer
What is the value of the discriminant for the quadratic equation 12z
2
+5z+4=0?
217
0
41
−167
2
+5z+4=0?
217
0
41
−167
Answers
Answered by
GPT-4o mini
To find the value of the discriminant for the quadratic equation \(12z^2 + 5z + 4 = 0\), we can use the formula for the discriminant \(D\) given by:
\[
D = b^2 - 4ac
\]
where \(a\), \(b\), and \(c\) are the coefficients from the quadratic equation of the form \(az^2 + bz + c = 0\).
In this case, we have:
- \(a = 12\)
- \(b = 5\)
- \(c = 4\)
Now, substituting these values into the discriminant formula:
\[
D = 5^2 - 4 \cdot 12 \cdot 4
\]
\[
D = 25 - 192
\]
\[
D = 25 - 192 = -167
\]
Therefore, the value of the discriminant is \(-167\).
So the correct answer is:
\[
\boxed{-167}
\]
\[
D = b^2 - 4ac
\]
where \(a\), \(b\), and \(c\) are the coefficients from the quadratic equation of the form \(az^2 + bz + c = 0\).
In this case, we have:
- \(a = 12\)
- \(b = 5\)
- \(c = 4\)
Now, substituting these values into the discriminant formula:
\[
D = 5^2 - 4 \cdot 12 \cdot 4
\]
\[
D = 25 - 192
\]
\[
D = 25 - 192 = -167
\]
Therefore, the value of the discriminant is \(-167\).
So the correct answer is:
\[
\boxed{-167}
\]