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

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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)   (Show Source): You can put this solution on YOUR website!
The quadratic factor is positive everywhere.


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,,...... , 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.

;
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

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