Question

I can't figure out how to get rid of a square root in a problem like such if i'm trying to find the x-intercept: x*sqrt(3-x)=0...how do you come up with the points 0,3???

Answer 1

You don't need to. Zero product property tells us that one or both of the factors has to be equal to zero. So
x=0
sqrt(3-x)=0 => x=-3

Answer 2

So I could sqrt both sides, subtract the three leaving me -x=-3, then divide by -1 to get a positive 3?

Answer 3

For the sqrt(3-x)=0, you can square both sides. Then do what you said

Answer 4

what about the x on the outside of the sqrt(3-x) though?

Answer 5

Oh, since you have a product. x times sqrt(3-x) and you want it to equal to zero. You want one or both of them to be zero. So you look at both cases.

If the x outside is 0, then x=0
if the sqrt(3-x) is zero, then x=3
So both of these are your answer

Answer 6

ok so the x on the outside is zero b/c the zero product property states that one or both x's =0. ok so then you're left with sqrt(3-x)=0 and you would sqrt both sides, then subtract the 3 and divide by -1 to get a positive 3?

Answer 7

zero product property states that one or both of the factors is zero. So x=0 or sqrt(3-x)=0. So you would square both sides, then subtract the 3 and divide by -1 to get a positive 3

Answer 8

got it!!! thank you so much!

Answer 9

No problem