Atmospheric carbon dioxide levels continue to increase and are suspected to contribute to global warming. The solution to the polynomial equation
x3 – 380x2 + 2x – 760 = 0
gives the record high amount of carbon dioxide in parts per million (ppm) in 2005, as measured at Mauna Loa Observatory. Determine this record amount.
x^3+380x^2+2x+760=0
x^2(x+380)+2(x+380)=0
(x+380)(x^2+2)=0
x=-380 as x^2is not equal to zero
Please advise if I am on the right track for solving this problem
why did you switch signs ???
x3 – 380x2 + 2x – 760 = 0
x^2(x - 380) + 2(x - 380) = 0
(x - 380)(x^2 + 2) = 0
x = 380 or x^2 = -2 , the latter has x not a real number
so x = + 380
Yes, you are on the right track for solving the problem. You correctly factored the polynomial equation:
x^3 – 380x^2 + 2x – 760 = 0
into its factored form:
(x + 380)(x^2 + 2) = 0
You correctly recognized that the first factor (x + 380) equals zero when x = -380.
However, you missed the fact that the second factor (x^2 + 2) cannot equal zero, which means there are no additional solutions for x other than x = -380.
Therefore, the record amount of carbon dioxide in parts per million (ppm) in 2005, as measured at Mauna Loa Observatory, is 380 ppm.