Problem Statement
Solve the following quadratic equation and give your answer correct to two decimal places:
$x^2 - 4x - 8 = 0$
Verified Solution & Marking Scheme
Apply Quadratic Formula
Here $a = 1, b = -4, c = -8$.
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-8)}}{2(1)} = \frac{4 \pm \sqrt{16 + 32}}{2} = \frac{4 \pm \sqrt{48}}{2}$
Simplify Radical
$\sqrt{48} = 4\sqrt{3} \approx 4(1.73205) = 6.9282$
$x = \frac{4 \pm 6.9282}{2} = 2 \pm 3.4641$
Compute Both Roots to Two Decimals
$x_1 = 2 + 3.4641 = 5.4641 \approx 5.46$
$x_2 = 2 - 3.4641 = -1.4641 \approx -1.46$