SOLUTION: The roots of the equation 2x squared-10x+8=0 represent the dimension of the rectangle. what is the area of the rectangle

Question 274322: The roots of the equation 2x squared-10x+8=0 represent the dimension of the rectangle. what is the area of the rectangle
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
For more help, check out this quadratic formula solver.

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=2, b=-10, and c=8

Negate -10 to get 10

Square -10 to get 100 (note: remember when you square -10, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator

Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator

Divide

So another answer is

So our solutions are:

or

Since the roots are or , this means that the length is 4 units and the width is 1 unit. So the area is simply A=4*1=4 square units.
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