Question

Question

Answer 1

Answer:

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

Step-by-step 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:

$ax^{2} + bx + c, a\neq0$.

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:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

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

$\Delta = (-24)^{2} - 4*1*144 = 0$

$x_{1} = \frac{24 + \sqrt{0}}{2} = 12$

$x_{2} = \frac{24 - \sqrt{0}}{2} = 12$

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