Sure, let's find the discriminant of the given quadratic equation [tex]\( 0 = -x^2 + 4x - 2 \)[/tex].
We know that the quadratic equation is generally represented as [tex]\( ax^2 + bx + c = 0 \)[/tex].
For the given equation [tex]\( 0 = -x^2 + 4x - 2 \)[/tex]:
- [tex]\( a = -1 \)[/tex]
- [tex]\( b = 4 \)[/tex]
- [tex]\( c = -2 \)[/tex]
The discriminant [tex]\( \Delta \)[/tex] for the quadratic equation [tex]\( ax^2 + bx + c = 0 \)[/tex] is calculated using the formula:
[tex]\[ \Delta = b^2 - 4ac \][/tex]
Substituting the values [tex]\( a = -1 \)[/tex], [tex]\( b = 4 \)[/tex], and [tex]\( c = -2 \)[/tex] into the formula, we get:
[tex]\[ \Delta = 4^2 - 4(-1)(-2) \][/tex]
First, calculate [tex]\( b^2 \)[/tex]:
[tex]\[ 4^2 = 16 \][/tex]
Next, calculate [tex]\( 4ac \)[/tex]:
[tex]\[ 4 \cdot (-1) \cdot (-2) = 8 \][/tex]
Now, subtract [tex]\( 4ac \)[/tex] from [tex]\( b^2 \)[/tex]:
[tex]\[ \Delta = 16 - 8 = 8 \][/tex]
Therefore, the discriminant of the quadratic equation [tex]\( 0 = -x^2 + 4x - 2 \)[/tex] is [tex]\(\boxed{8}\)[/tex].
