The equation x³ + 3x² = 4 models the volume of a shipping container where x is the width. Graph the equation to find the width of the box.

Question

a. 4 ft

b. 2 ft

c. 8 ft

d. 1 ft

I have tried this but sometimes it gets too confusing, I need help.

Answer 1

The result is a cubic polynomial. I used the powerful math Web site, Wolfram Alpha, to calculate the roots of the polynomial - although I could do it by hand (and you could too), I didn't do it by hand in this case because it's your time, not mine, that I'm spending. LOL Pro Tip: use Wolfram Alpha when you can't solve a problem in your head, and you can't figure out how to program a calculator to do it for you. But because Wolfram Alpha gives you more information than a numerical answer, use the result on screen - more info than you need, usually - to help you to understand the problem better, and prepare you for the day when you must solve by hand.

So the roots of the polynomial (where f(x) goes to zero): one at x = 1 and two at x = -2. When x = 0, y = -4. The roots are what matters, because they represent the box width. You can't have a negative width, so...

x = 1 is the answer.