Joe wants to know the dimensions of his rectangular flat screen TV if its area measures 48 square cacti cand represented by the quadratic expression x 8x how long is Joey's TV?

Answer 1

To find the dimensions of Joe's rectangular flat screen TV, we need to solve the quadratic equation given by the expression for the area, which is 48 square cacti.

We have the expression for the area as:

x² + 8x = 48

First, we can rearrange the equation to set it to 0:

x² + 8x – 48 = 0

Next, we will use the quadratic formula to solve for x: The quadratic formula is given by:

x = – b ± √b² – 4ac

¯¯¯ ¯¯2a¯¯¯¯¯¯¯¯

Where a = 1, b = 8, and c = – 48.

Now, we calculate:

1.) b² = 8² = 64

2.) 4ac = 4 x 1 x ( – 48) = – 192

3.) Therefore, b² – 4ac = 64 + 192 = 256

Now, we plug these values into the quadratic formula:

x = – 8 ± √ 256

2 x 1

x = – 8 ± 16

2

Now we will calculate the two possible values of x:

1.) x = – 8 + 16 = 8⁄2 = 4

2

2.) x = – 8 – 16 = –24⁄2 = –12 (not a valid solution since dimensions cannot be negative)

2

Thus, the length of Joe's TV, represented by x, is 4 cacti.

If Joe wants the other dimension, we can use the area formula with the length we've found: Area = length × width => 48 = 4 x width.

Solving for width, we have:

width = 48⁄4 = 12

cacti.

So, the dimensions of Joe's TV are:

Length = 4 cacti

Width = 12 cacti