Given :
Population of country in 2006 , P = 300 million.
Consumption of fruit juice in 2006 by while population, C = 1.85 billion.
To Find :
The average number of gallons of fruit juice consumed per person in the country in 2006.
Solution :
We know, 1 billion = 1000 million.
C = 1.85 billion = 1850 million.
Now, average umber of gallons of fruit juice consumed per person in the country in 2006 is :
Hence, this is the required solution.
one way would be to factor
I can't factor it so we will have to use Descartes' Rule of Signs which is helpful for finding how many real roots you have
it goes like this:
for a polynomial with real coefients, consider .
after arranging the terms in decending order in terms of degree, count how many times the signs of the coeffients change direction and minus 2 from that number until you get to 1 or 0. that will be the number of even roots the function can have
We have (-, -, +, +). the signs changed 1 times, so it has 1 real positive root
to get the negative roots, we evaluate f(-x) and see how many times the root changes
signs are (-, -, -, +). there was 1 change in sign
so the function has 1 real negative root
a total of 2 real roots
a function of degree can have at most,
roots
our function is degree 6 so it has 6 roots
if 2 are real, then the others must be complex
6-2=4 so there are 4 complex roots
you can also show that there are only 2 real roots by using a graphing utility to see that there are only 2 real roots
By the quadratic formula,
Then
Multiply numerator and denominator by the denominator's conjugate: