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

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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) About Me  (Show Source):
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Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 2%2Ax%5E2-10%2Ax%2B8=0 ( notice a=2, b=-10, and c=8)





x+=+%28--10+%2B-+sqrt%28+%28-10%29%5E2-4%2A2%2A8+%29%29%2F%282%2A2%29 Plug in a=2, b=-10, and c=8




x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%2A2%2A8+%29%29%2F%282%2A2%29 Negate -10 to get 10




x+=+%2810+%2B-+sqrt%28+100-4%2A2%2A8+%29%29%2F%282%2A2%29 Square -10 to get 100 (note: remember when you square -10, you must square the negative as well. This is because %28-10%29%5E2=-10%2A-10=100.)




x+=+%2810+%2B-+sqrt%28+100%2B-64+%29%29%2F%282%2A2%29 Multiply -4%2A8%2A2 to get -64




x+=+%2810+%2B-+sqrt%28+36+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




x+=+%2810+%2B-+6%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2810+%2B-+6%29%2F4 Multiply 2 and 2 to get 4


So now the expression breaks down into two parts


x+=+%2810+%2B+6%29%2F4 or x+=+%2810+-+6%29%2F4


Lets look at the first part:


x=%2810+%2B+6%29%2F4


x=16%2F4 Add the terms in the numerator

x=4 Divide


So one answer is

x=4




Now lets look at the second part:


x=%2810+-+6%29%2F4


x=4%2F4 Subtract the terms in the numerator

x=1 Divide


So another answer is

x=1


So our solutions are:

x=4 or x=1





Since the roots are x=1 or x=4, 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.