A small company borrows money and remains in debt to its lenders for a period of time. The function f(x)=−4x2+10x+60 represents the amount of debt the company has, in thousands of dollars, x years after opening its business. Approximately how many years after opening its business will the company be out of debt?

4.7 years

5.3 years

5.8 years

6.4 years

The number of years after opening its business the company will be out of debt 5.3 years

Step-by-step explanation:

Given

The function f(x)=−4x² + 10x + 60

For the company to be out of debt, then the function must be at least 0

The expression for this is f(x) ≥= 0.

But, we'll be working with the least number of years.

So, we'll make use of f(x) = 0;

Substitution 0 for f(x) in the function

f(x)= −4x² + 10x + 60 becomes

0 = −4x² + 10x + 60 --------- Reorder

4x² - 10x - 60 = 0 ----- Solving this quadratic equation, we have

Where a = 4, b = -10 and c = -60

By Substitution, we have

or  

or  

or  

But number of years can't be negative;

So,   years.

Hence, the number of years after opening its business the company will be out of debt 5.3 years

72 is the answer to this problem