Question

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

x^2−2x−4=0



Enter your answers in the boxes.

x = or x =

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))