ANSWER
The discriminant is zero.
The given equation has one real root.
EXPLANATION
The given quadratic equation is:
[tex] - 2 {x}^{2} = - 8x + 8[/tex]
We rewrite this in the form;
[tex]a {x}^{2} + bx + c = 0[/tex]
[tex]- 2 {x}^{2} + 8x - 8 = 0[/tex]
This means that,
a=-2, b= 8, c=-8
The discriminant is given by;
D=b² - 4ac
That is:
[tex]D = {8}^{2} - 4( - 2)( - 8)[/tex]
[tex]D = 64 - 64 = 0[/tex]
Therefore the discriminant is zero.
This tells us that the quadratic equation has one real root.
In order words, the given quadratic equation has a repeated real root.
