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

Solution:

Given: Function f(x) = x² + 8x + 4

The zeros of a function can be defined as the values for x for which the function terminates to zero.

We can find zeros/roots by using quadratic formula

x= -b ± √(b² - 4ac) / 2a

Here a = 1, b = 8, c = 4

x = [-8 ± √(8² - 4(4)) ]/ 2(1)

x = [-8 ± √(64 - 16)]/ 2

x = [-8 ± √48] / 2

x = -8/2 ±4 √3/2

x= -4 ± 2 √3

The zeros of the given function are (-4 + 2 √3) and (-4 - 2 √3).

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

Summary:

The zeros of the function f(x) = x² + 8x + 4, expressed in simplest radical form are (-4 + 2 √3) and (-4 - 2 √3).