Question

Find the discriminant.

2z^2 - 6z + 8 = 0

Answer 1

To find the discriminant of the quadratic equation \( 2z^2 - 6z + 8 = 0 \), we can use the formula for the discriminant, which is given by:

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

where \( a \), \( b \), and \( c \) are the coefficients from the standard quadratic equation \( az^2 + bz + c = 0 \).

From the equation \( 2z^2 - 6z + 8 = 0 \), we identify the coefficients as:
- \( a = 2 \)
- \( b = -6 \)
- \( c = 8 \)

Now, we can substitute these values into the discriminant formula:

\[
D = (-6)^2 - 4 \cdot 2 \cdot 8
\]

Calculating \( (-6)^2 \):

\[
(-6)^2 = 36
\]

Now calculating \( 4 \cdot 2 \cdot 8 \):

\[
4 \cdot 2 \cdot 8 = 64
\]

Now we can substitute these results back into the discriminant formula:

\[
D = 36 - 64
\]

Calculating \( 36 - 64 \):

\[
D = -28
\]

Thus, the discriminant of the equation \( 2z^2 - 6z + 8 = 0 \) is

\[
\boxed{-28}
\]