SOLUTION: Find and graph the solution of: x^4 (less than or equal to) 10x^2-9. I dont even know what steps to take to begin solving this problem. thank you.

Algebra ->  Coordinate-system -> SOLUTION: Find and graph the solution of: x^4 (less than or equal to) 10x^2-9. I dont even know what steps to take to begin solving this problem. thank you.      Log On


   

Question 932930: Find and graph the solution of: x^4 (less than or equal to) 10x^2-9.
I dont even know what steps to take to begin solving this problem. thank you.
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4%3C=10x%5E2-9

x%5E4-10x%5E2%2B9%3C=0, from additive inverse application. You know what the basic shape will be, so just find the roots. You should check first for factorability.

%28x%5E2-1%29%28x%5E2-9%29%3C=0
And you can do more;
%28x-1%29%28x%2B1%29%28x-3%29%28x%2B3%29%3C=0.

The solution, and roots, are -3, -1, 1, 3. That is "OR". You'll need to check the intervals carefully to know just how the graph goes around the -1 and the 1. Use arithmetic to check this as a help in making the graph.....

This is a graph of the polynomial function, NOT the actual inequality:
graph%28300%2C300%2C-6%2C6%2C-12%2C12%2Cx%5E4-10x%5E2%2B9%29