Question 583110: solve the inequality using interval notation for x^4 + 5x^3 -16x^2-80x <0
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! solve the inequality using interval notation for
x^4 + 5x^3 -16x^2-80x <0
x(x^3 + 5x^2 -16x-80) <0
x(x^2(x+5) -16(x+5)) <0
x(x+5)(x^2-16)<0
x(x+5)(x+4)(x-4)<0
draw zeros on number line:
<....+....-5....-....-4.....+....0.....-....4.....+....>
solution: (-5,-4) U (0,4)
Explanation for number line:
By Inspection it can be seen that when x>4, function is >0.
Moving to the left thru the zeros, sign of the intervals switch when going thru a zero of odd multiplicity like 1, 3, 5, etc. All zeros are of multiplicity 1, thus the switching of interval signs.
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