Answer:
x = - 4 ± 2
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 = ± = ± 2
( subtract 4 from both sides )
x = - 4 ± 2
Thus the zeros are
x = - 4 - 2 and x = - 4 + 2
The shortest length of the fence used by the rancher in a rectangular field of 1000000 square feet is 4899 ft.
<h3>What is the area of a rectangle?</h3>The area of a rectangle is a region enclosed in four corners where two opposite sides are equal. The area of the rectangle is mathematically expressed as:
Area of a rectangle = length(x) × breath(y)
1000000 sq.ft = (x) × (y) ---- (1)
However, to determine the fencing, we have:
Length of fencing = 2x + 2y
Suppose we use the x-direction to estimate the region where the fencing is located, we have:
Length of fencing = 2x + 2y + x
Length of fencing = 3x + 2y ---- (2)
From equation (1), make (y) the subject of the formula and replace the value of y with equation (2)
The Length of fencing is:
Now, if we replace the value with equation (1), then y will be:
Now, the shortest length of the fencing can be computed by using the equation (2):
L = 3x + 2y
Learn more about the area of a rectangle here: