Question

Question
Solve the quadratic equation y=x2−8x+20
. Show your work by using the quadratic formula. Write your answers in the form x=a±bi
.(4 points)

Answer 1

We solve x^2 − 8x + 20 = 0 with the quadratic formula x = [−b ± sqrt(b^2 − 4ac)]/(2a). Here a = 1, b = −8, c = 20.

Compute:
b^2 − 4ac = (−8)^2 − 4(1)(20) = 64 − 80 = −16
sqrt(b^2 − 4ac) = sqrt(−16) = 4i

So
x = [−(−8) ± 4i]/(2·1) = [8 ± 4i]/2 = 4 ± 2i.

Answer: x = 4 ± 2i.