Mathematics 35 Online
OpenStudy (anonymous):

find the points of intersection. y = x^3, y = 2x

OpenStudy (anonymous):

3 points. 1) (0,0) 2) (-1.4,-2.8) 3) (1.4,2.8)

OpenStudy (anonymous):

abe you're really not helping me by giving me the answers. i have the answers. thats not the problem. i dont know how to get them.

OpenStudy (anonymous):

Do you have a graphing calculator?

OpenStudy (anonymous):

yes but i still have to show my work. i cant just put it in and get the answers that way

OpenStudy (anonymous):

Those aren't right completely. This is how you do it. x^3 = 2x x^3 - 2x = 0 factor out an x x (x^2 - 2) = 0 realize that x = 0 is now an answer divide by x x^2 -2 = 0 quadratic equation gives you $\sqrt{2}$ as an X answer. plug into either original equation to get 2$\sqrt{?}$ as the Y. both negative is also an answer.

OpenStudy (anonymous):

the script got messed up. Near the end it is supposed to say plug into either original equation to get $2\times \sqrt{2}$

OpenStudy (anonymous):

how do you know there aren't more answers? from checking?

OpenStudy (anonymous):

2xroot2 is 2.82...

OpenStudy (anonymous):

an equation with x^3 can only have a maximum of 3 intersection points with a straight line.

OpenStudy (anonymous):

okay, but how do you know its not $(-\sqrt{2}, 2\sqrt{2})$

OpenStudy (anonymous):

like how do you know they're both positive and both negative

OpenStudy (anonymous):

look at the question. it is asking when those two equations hit each other. so, any answer you come up with has to be a point on BOTH lines. plug those points into EITHER equation and you will realize it doesn't work for either x^3 or 2x.

OpenStudy (anonymous):

okay, i understand

OpenStudy (anonymous):

a negative X times 2 or to the third, either way will stay negative and your Y is positive. how could that point possibly work.

OpenStudy (anonymous):

good stuff :)

OpenStudy (anonymous):

it was just a random thought as to know how to not get too many answers.

OpenStudy (anonymous):

You can never get too many answers because if they shouldn't be there, they won't work if you plug them in! :)

OpenStudy (anonymous):

ok :)