Math question involving polynomials

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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 $x^2-110x+1000=0$ 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 $-5(x-a)=0$ then $(x-a)=0$ .

$\frac{0}{-5}=0~.$
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?
$x^2-110x+1000=(x-10)(x-100)$
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!