Problem Statement
Solve the quadratic equation $x^2 - 4x - 8 = 0$ using the quadratic formula. Give your answers correct to two decimal places (use $\sqrt{3} \approx 1.732$).
Verified Solution & Marking Scheme
Identify coefficients and discriminant
$$a = 1, \quad b = -4, \quad c = -8$$
$$D = b^2 - 4ac = (-4)^2 - 4(1)(-8) = 16 + 32 = 48$$
Apply Quadratic Formula
$$x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-(-4) \pm \sqrt{48}}{2(1)} = \frac{4 \pm 4\sqrt{3}}{2} = 2 \pm 2\sqrt{3}$$
Compute numerical roots to 2 decimal places
$$x_1 = 2 + 2(1.732) = 2 + 3.464 = 5.464 \approx 5.46$$
$$x_2 = 2 - 2(1.732) = 2 - 3.464 = -1.464 \approx -1.46$$