Question 1196593: 4x^2+5x-9 over x^2-x - 6 ≥ 0
Found 2 solutions by greenestamps, MathTherapy:
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
*** Revised to correct silly arithmetic error....***
To find where the inequality is satisfied, we need to determine the values of x where the sign of the function changes; that can happen only at values of x for which the numerator and/or denominator is 0.
So factor the numerator and denominator to identify those values of x.
The function value is 0 and changes sign when the numerator is 0 -- at x = -9/4 and x = 1.
The function is undefined and its value changes sign when the denominator is 0 -- at x = -2 and x = 3.
For "large" values of x (greater than 3), all the factors in the factored form of the function are positive, so the function value is positive.
And the function value changes sign at x = -9/4, -2, 1, and 3. That means the function value is...
positive for x greater than 3;
negative for x between 1 and 3;
positive for x between -2 and 1;
negative for x between -9/4 and -2; and
positive for x less than -9/4
Finally, remembering that the function is 0 at -9/4 and 1 and undefined at -2 and 3, the solution set to the inequality is
(-infinity,-9/4] U (-2,1] U (3,infinity)
Answer by MathTherapy(10551)  (Show Source):
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