Question

Question

Todd travels frequently for his business. For tax reasons, he wants to use up all of the remaining money in his business travel fund this
year. He uses the function f (x) = x2 24x + 144 to determine how many trips he must take to spend all of his
remaining business travel funds. In this function, Xrepresents the number of trips and f (x)is the amount of money left in his fund
after the trips.

Answer 1

One real zero solution, as
`\Delta` is 0, and he must take 12 trips.

Explanation:

His amount of funds is given by:

`f(x) = x^2 + 24x + 144`

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

`ax^(2) + bx + c, a\\eq0`.

This polynomial has roots
`x_(1), x_(2)` such that
`ax^(2) + bx + c = a(x - x_(1))*(x - x_(2))`, given by the following formulas:

`x_(1) = (-b + √(\Delta))/(2*a)`

`x_(2) = (-b - √(\Delta))/(2*a)`

`\Delta = b^(2) - 4ac`

How many trips he must take to spend all of his remaining business travel funds?

x trips, and x is found when f(x) = 0. So

`x^2 - 24x + 144 = 0`

Quadratic equation with
`a = 1, b = -24, c = 144`

So

`\Delta = (-24)^(2) - 4*1*144 = 0`

`x_(1) = (24 + √(0))/(2) = 12`

`x_(2) = (24 - √(0))/(2) = 12`

One real zero solution, as
`\Delta` is 0, and he must take 12 trips.