Question

What are the zeros of the function f(x) = x2 + 8x +4, expressed in simplest radical form?

x=-4+2/3
x=-41/48
x= -8173
x= -45473

Answer 1

x = - 4 ± 2
`√(3)`

Explanation:

Given

f(x) = x² + 8x + 4

To find the zeros let f(x) = 0, that is

x² + 8x + 4 = 0 ( subtract 4 from both sides )

x² + 8x = - 4

To solve using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(4)x + 16 = - 4 + 16

(x + 4)² = 12 ( take the square root of both sides )

x + 4 = ±
`√(12)` = ± 2
`√(3)` ( subtract 4 from both sides )

x = - 4 ± 2
`√(3)`

Thus the zeros are

x = - 4 - 2
`√(3)` and x = - 4 + 2
`√(3)`