SOLUTION: Please help me to complete this problem: "The formula N=4x^2+5x+2 represents the number of households N, in thousands, in a certain city that have a computer x years after 1990. Ac

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Question 42351: Please help me to complete this problem: "The formula N=4x^2+5x+2 represents the number of households N, in thousands, in a certain city that have a computer x years after 1990. According to the formula, in what year were there 127 thousand households with computers in this city?"
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
We know 'N' and have to find 'x'.

The question actually demands the solving of the quadratic equation formed when 'N' is 127 in the equation N=4x%5E2%2B5x%2B2.

So the quadratic equation to be solved is
127=4x%5E2%2B5x%2B2
or 4x%5E2%2B5x%2B2-127=0
or 4x%5E2%2B5x-125=0
or 4x%5E2-20x%2B25x-125=0
or 4x%28x-5%29%2B25%28x-5%29=0
or %28x-5%29%284x%2B25%29=0

As product of two quantities is zer so at least one must be zero.
Hence, either (x - 5) = 0 i.e. x = 5 or (4x + 25) = 0 i.e. x+=+-25%2F4.

Now, 'x' represents no. of years after 1990 so if x < 0, then it represents no. of years before 1990 and then the given equation is not valid.

The year x = 5 refers to (1990 + 5 =) 1995.
Hence the number of households was 127 thousands in 1995.