Vieta's formulas for quadratic polynomials:
For a quadratic polynomial $ax^2 + bx + c$:
Sum of roots $\alpha + \beta = -\frac{b}{a}$.
Product of roots $\alpha \beta = \frac{c}{a}$.
Here, $a = 1$, $b = -2$, and $c = -8$:
Sum $= -\frac{-2}{1} = 2$.
Product $= \frac{-8}{1} = -8$.

Option breakdown:

• $2, 8$ has the wrong sign for the product.
• $-2, 8$ has reversed signs for both sum and product.
• $-2, -8$ has the wrong sign for the sum.
• $2, -8$ is the exact sum and product of the roots.