SOLUTION: Solve the inequality. (x - 5)(x^2 + x + 1) > 0 a. (-∞, -1) or (1, ∞) b. (-1, 1) c. (-∞, 5) d. (5, ∞)

Algebra ->  Functions -> SOLUTION: Solve the inequality. (x - 5)(x^2 + x + 1) > 0 a. (-∞, -1) or (1, ∞) b. (-1, 1) c. (-∞, 5) d. (5, ∞)       Log On


   

Question 1061025: Solve the inequality.
(x - 5)(x^2 + x + 1) > 0
a. (-∞, -1) or (1, ∞)
b. (-1, 1)
c. (-∞, 5)
d. (5, ∞)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The quadratic factor is positive everywhere.
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E2%2Bx%2B1%29

You could try putting it into standard form, or you can just check its discriminant to see if this is negative or not. You should find that the discriminant,,...... 1%5E2-4%2A1%2A1=1-4=-3%3C0, so this means the quadratic factor as a function will not have points on the x-axis....

That then leaves you with the critical x value for the linear factor, and that is at x=5.

linearFactor%2AquadraticFactor%3E0;
Check the signs in the indicated intervals to see which interval makes the inequality true and which make it false. 

INTERVAL          ANALYZE INEQUALITY     RESULT
(-infin,5)        (-)(+)>0,  FALSE       FALSE
(5,infinity)      (+)(+)>0,  TRUE        TRUE