Question

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

Answer 1

Answer:

x = - 4 ± 2$\sqrt{3}$

Step-by-step 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 = ± $\sqrt{12}$ = ± 2$\sqrt{3}$ ( subtract 4 from both sides )

x = - 4 ± 2$\sqrt{3}$

Thus the zeros are

x = - 4 - 2$\sqrt{3}$ and x = - 4 + 2$\sqrt{3}$