Question

Use the quadratic formula to determine the exact solutions to the equation.

Answer 1

For this case we have the following equation:
 x ^ 2-2x-4 = 0
 We use the quadratic formula:
 x = (- b +/- root (b ^ 2 - 4 * a * c)) / (2 * a)
 Substituting values we have:
 x = (- (- 2) +/- root ((- 2) ^ 2 - 4 * (1) * (- 4))) / (2 * (1))
 Rewriting we have:
 x = (2 +/- root (4 + 16)) / 2
 x = (2 +/- root (20)) / 2
 x = (2 +/- root (4 * 5)) / 2
 x = (2 +/- 2raiz (5)) / 2
 x = (1 +/- root (5))
 The roots are:
 x1 = (1 + root (5))
 x2 = (1 - root (5))
 Answer:
 x1 = (1 + root (5))
 x2 = (1 - root (5))