SOLUTION: i need to solve this inequality and i don't know how to solve it : x^4-5x^3-25x^2+65x+84(greater than or equal to)0
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Question 483457: i need to solve this inequality and i don't know how to solve it : x^4-5x^3-25x^2+65x+84(greater than or equal to)0 Found 2 solutions by stanbon, MathLover1:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! x^4-5x^3-25x^2+65x+84(greater than or equal to)0
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Find the zeroes:
Use synthetic division:
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-1)....1....-5....-25.....65....84
.......1.....-6....-19......84...|..0
7).....1......1.....-12....|..0
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Solve x^2+x-12 = 0
(x+4)(x-3) = 0
x = -4 or x = 3
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Draw a number line and plot x = -4,-1,3,7
These values satisfy the EQUALITY.
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Test a value in each of the 5 intervals to find the solution set:
INEQUALITY: (x+4)(x+1)(x-3)(x-7) > 0
Let x = -10 to get -*-*-*- > 0 ; true
Let x = -2 to get +*-*-*- > 0 ; false
Let x = 2 to get +*+*-1*- > 0 ; true
Let x = 5 to get +*+*+*- > 0 ; false
Let x = 10 to get +*+*+*+ > 0 ; true
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Solution: (-oo,-4]U[-1,3]U[7,+oo)
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Cheers,
Stan H.
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