Question

A small company borrows money and remains in debt to its lenders for a period of time. The function f(x)=−6x2+8x+50 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?

A. 2.9
B. 3.2
C. 3.6
D. 4.2

Answer 1

Given that the debt has been represented by the function:
f(x)=-6x^2+8x+50
To get the number of years, x that it would take for the company to be debt free we proceed as follows:
we solve the equation for f(x)=0
hence:
0=-6x^2+8x+50
solving for x using the quadratic formula we get:
x=[-b+/-sqrt(b^2-4ac)]/2a
x=[-8+/-sqrt(8^2-4*(-6)*50)]/(-6*2)
x=[-8+/-√1264]/(-12)
x=27.552
x~28