The yearly profit of a company in thousands of dollars can be modeled by P (t) = t^4 - 5t^2 + 4, where t is the number of years since 2000. Factor to find the years in which the profit was 0.

When the profit is 0; then P (t) = 0

You have this equation:

t⁴-5t²+4=0

Then, you have to do the following change:

t²=z

you have this other equation:

z²-5t+4=0

Now, you can solve this square equation:

z=[5⁺₋√ (25-16) ]/2 = (5⁺₋√9) / 2=

you have two solutions for z.

z₁ = (5-3) / 2=1

z₂ = (5+3) / 2=4

Now; if z=1; then

t²=z

t²=1

t=⁺₋√1

We have two solutions:

t=-1 this is not a valid solution:

t=1;

Then in 2001 (2000+t=2000+1=2001) the profit was 0.

If z=4, then:

t²=z

t²=1

t=⁺₋√4

We have two solutions:

t=-2 this is not a valid solution:

t=2;

Then in 2002 (2000+t=2000+2=2002) the profit was 0.

Answer: the yeares in which the profict was 0, were 2001 and 2002.