If x² - 8x - 9 = 0; values of x correct to one significant figure are :

1. 9 and -1

2. 9 or -1

3. 9.0 or -1.0

4. 9.00 or -1.00

Comparing equation x² - 8x - 9 = 0 with ax² + bx + c = 0, we get :

a = 1, b = -8 and c = -9.

By formula,

x = $\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Substituting values we get :

$x = \dfrac{-(-8) \pm \sqrt{(-8)^2 - 4 \times 1 \times -9}}{2 \times 1} \\[1em] = \dfrac{8 \pm \sqrt{64 + 36}}{2} \\[1em] = \dfrac{8 \pm \sqrt{100}}{2} \\[1em] = \dfrac{8 \pm 10}{2} \\[1em] = \dfrac{8 + 10}{2} \text{ or } \dfrac{8 - 10}{2} \\[1em] = \dfrac{18}{2} \text{ or } \dfrac{-2}{2} \\[1em] = 9 \text{ or } -1$

Hence, Option 2 is the correct option.