Question

Can anyone help me solve this? X^2-10x+12≤0

Answer 1

A warm Welcome to OpenStudy. I can help guide you through this useful site. You can ask your questions to me or you can message me. Please use the chat for off topic questions. Remember to give the person who helped you a medal by clicking on "Best Answer". We follow a code of conduct, ( http://openstudy.com/code-of-conduct ). Please take a moment to read it.

Answer 2

Ok, so you have a quadratic inequality. You want to find the solutions less than or equal to 0.

First, find your factors:
Let's just say its equal to 0 for a second, although its not
x^2-10x+12=0
x^2-10x +(-5)^2=-12+25
(x-5)^2 = 13
x-5 = ±√13
x= 5±√13

Back to our inequality:
We can now set our factors less than or equal to 0.
(x-5+√13)(x-5-√13)≤0
The easiest way to find the solution now, is make a sign diagram.
I am going to draw one now and attach it.

Answer 3

So, essentially, with a sign diagram, you want to write out your factors and list all the intervals around the zeros. Once you have done that, you fill in the sign, plus or minus, for each factor in that interval. Then, you add the signs to find the sign of the two multiplied together, the quadratic.
Once you have made your diagram, or chart as you might call it, then find the interval where your sign matches the original inequality statement.
In this case, that would be, (5-√13, 5+√13). However, we're allowed to have x equal zero here. So we, instead, have closed brackets, [5-√13, 5+√13]
This is because x is zero at both 5-√13 and 5+√13

Answer 4

So your answer is x≤0 at [5-√13, 5+√13]

Answer 5

Does this make sense?

Answer 6

thanks :)

Answer 7

You understand how to do a sign chart now?

Answer 8

yes, I undarsand, thaks a lot for your help :)

Answer 9

Ok, no problem. Good luck!