Solve the problem.
-The formula $\mathrm { N } = 4 \mathrm { x } ^ { 2 } + 3 \mathrm { x } + 1$ represents the number of households $\mathrm { N }$, in thousands, in a certain city that have a computer x years after 1990 . According to the formula, in what year were there 77 thousand households with computers in this city?
A) 1994
B) 1993
C) 1992
D) 1995

Question

Quizplus · Accepted Answer

The formula is $\mathrm { N } = 4 \mathrm { x } ^ { 2 } + 3 \mathrm { x } + 1$. To find the year when there were 77 thousand households with computers, we need to solve the equation $\mathrm { N } = 77$. Substituting $\mathrm { N } = 77$ into the formula, we get:$$77 = 4 \mathrm { x } ^ { 2 } + 3 \mathrm { x } + 1$$$$4 \mathrm { x } ^ { 2 } + 3 \mathrm { x } - 76 = 0$$$$(4 \mathrm { x } - 4)( \mathrm { x } + 19) = 0$$$$\mathrm { x } = 1 \text{ or } \mathrm { x } = -19$$Since $\mathrm { x }$ represents the number of years after 1990, $\mathrm { x } = -19$ is not a valid solution. Therefore, $\mathrm { x } = 1$. This means that there were 77 thousand households with computers in this city 1 year after 1990, which is 1991.

Solve the Problem N=4x2+3x+1\mathrm { N } = 4 \mathrm { x } ^ { 2 } + 3 \mathrm { x } + 1N=4x2+3x+1

Solve the Problem $\mathrm { N } = 4 \mathrm { x } ^ { 2 } + 3 \mathrm { x } + 1$