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Question 644950: Find all real zeros of the function:
h(x)= x^5+15x^4+72x^3+80x^2-225x-375
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find all real zeros of the function:
h(x)= x^5+15x^4+72x^3+80x^2-225x-375
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Use the rational roots theorem to solve:
....0...|....1......15......72.....80......-225......-375.............
....1...|....1......16......88.....168.....-57.......-432
...,2...|....1......17.....194....468.....711.......1047 (zero exists between 1 and 2)
....3...|....1......18.....126....458.....1149.....3072 (3 is upper boundary)
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..-1...|....1......14.....58.......22.....-247.....-128
..-2...|....1......13.....46.....-12.....-201.......27 (zero exists between -1 and -2)
..-3...|....1......12.....36.....-28.....-141......48
..-4...|....1......11.....28.....-32.....-119......101
..-5...|....1......10.....22.....-30.....-75..........0 (-5 is a root)
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..-5...|....1......5.......-3......-15......0 (-5 is a root of multiplicity 2)
h(x)=(x+5)(x+5)(x^3+5x^2-3x-15)
h(x)=(x+5)(x+5)(x^2(x+5)-3(x+5)
h(x)=(x+5)(x+5)(x^2-3)(x+5)
The 5 zeros are: -5 (multiplicity 3), √3 and -√3
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note: I had the help of a graphic computer program to check my answers.
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