# Math question involving polynomials

• May 7th 2011, 12:16 PM
Arise01
Math question involving polynomials
The profit, "P", of a video company (in thousands of dollars), is given by P(x) = -5x^2 + 550x - 5000, where x is the amount spent on advertising, in thousands of dollars.

a) Determine the amount spent on advertising that will result in a profit of $0. Ok so I started it here... 0 = -5x^2 + 550x - 5000 = -5(x^2 - 110x + 1000) I'm not sure how to continue from here. I'm pretty sure that I'm on the right track. I think that you have to find when x = 0. Essentially what I'm trying to do I think is find the x-intercepts. • May 7th 2011, 12:29 PM emakarov You have a quadratic equation. • May 7th 2011, 12:29 PM e^(i*pi) You're on the right track. First of all you can cancel out -5 to give$\displaystyle x^2-110x+1000=0$and solve the resulting quadratic using your favourite method . • May 7th 2011, 12:44 PM Arise01 What do you mean by "favourite method"? Oh wait a minute I think I know what to do. I'll use the formula that I just saw on the wiki link you gave me "emakarov". thanks. But firstly how do I cancel out -5? • May 7th 2011, 12:58 PM emakarov If you have an equation -5 * f(x) = 0 for some expression f(x), divide both sides by -5 to get f(x) = 0. • May 7th 2011, 01:04 PM Arise01 So it's just 0 = x^2 - 110x + 1000 ? • May 7th 2011, 02:22 PM emakarov Quote: Originally Posted by Arise01 So it's just 0 = x^2 - 110x + 1000 ? Yes. • May 7th 2011, 02:40 PM Arise01 but what happened to the -5? • May 7th 2011, 02:45 PM Plato Quote: Originally Posted by Arise01 but what happened to the -5? If we have$\displaystyle -5(x-a)=0$then$\displaystyle (x-a)=0$.$\displaystyle \frac{0}{-5}=0~.$• May 7th 2011, 02:47 PM Arise01 So I use the quadratic formula on x^2 - 110x + 1000 to solve for the x- intercepts? • May 7th 2011, 02:50 PM Plato Quote: Originally Posted by Arise01 So I use the quadratic formula on x^2 - 110x + 1000 to solve for the x- intercepts? Why not just factor it?$\displaystyle x^2-110x+1000=(x-10)(x-100)\$
• May 7th 2011, 02:53 PM
Arise01
Oh wow how could I miss that. So the x - intercepts are 10 and 100?
• May 7th 2011, 03:02 PM
Plato
Quote:

Originally Posted by Arise01
Oh wow how could I miss that. So the x - intercepts are 10 and 100?

Right on!