SOLUTION: How would I solve this polynomial inequality and put the solution set into interval notation? 9x^2 + 1 is greater than or equal to 6x

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Question 907261: How would I solve this polynomial inequality and put the solution set into interval notation?
9x^2 + 1 is greater than or equal to 6x
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
9x%5E2%2B1%3E=6x
9x%5E2-6x%2B1%3E=0

Roots are these.
%286-sqrt%2836-4%2A9%2A1%29%29%2F18 and %286%2Bsqrt%2836-4%2A9%2A1%29%29%2F18 which are equal because the discriminant is 0.
Only one root: 6%2F18=1%2F3.

The inequality is true for all real values of x.

graph%28300%2C300%2C-4%2C4%2C-2%2C4%2C9x%5E2-6x%2B1%29

You could factorize the quadratic trinomial, since you found the single root of x=1%2F3. Not so easy to recognize without actually evaluating the discriminant.

9%28x%5E2-%286%2F9%29x%2B1%2F9%29%3E=0
highlight%289%28x-1%2F3%29%5E2%3E=0%29